A few uses of elementary particles in nuclear structure studies

Acta Physica Academiae Scientiarum Hungaricae, Tomus 21 (3--4), pp. 255--276 (1966)

A F E W USES OF E L E M E N T A R Y PARTICLES IN NUCLEAR STRUCTURE STUDIES*

By

D. H. WILKII~SON

NUCLEAR PHYS[CS LABORATORY, OXFORD, ENGLAND

(Presented by L. J• -- Received 25.11. 1966)

A selective review is given of some of the ways in which "elementary particles "and the techniques of high energy physics in general may be used for the investigations of nuclear structure. It is pointed out that our ability to extract new nuclear structure information from such experiments is often limited by our present ignorance on other aspects of nuclear structure.

lntroduct ion

We are very familiar with the use of the great accelerating machines for

the s tudy of e lementary particles in their own right. Beatos of nucleons, pions,

muons, K-mesons, anti-protons, neutrinos and so on are generated and used to provoke collisions or reactions tha t brings us information about the element-

ary particles themselves. These same beams will, of course, interact also with

complex nuclei, and sometimes such interactions have been used either because targets of complex nuclei were demanded in order to get nucleons in sufficiently

concentra ted forro or, more rarely, because complex nuclei, by vir tue of the spin of some other quan tum number , enabled us to place restrictions on the

character of the e lementary particle interactions. However , the availabili ty

of such beams of e lementary particles na tura l ly leads us to ask the question whether, by their interact ion with complex nuclei, we may not be able to gain

information about the complex nuclei themselves of a character tha t cannot

be obtained by the normal methods of nuclear s t ructure exper imentat ion or tha t may perhaps confirm the results of such conventional methods of experi-

menta t ion from this novel point of view. So lar work has been confined to e lementary particle beatos tha t "na tur -

al ly" found themselves available from having been prepared for elementary

particles research purposes. We are now beginning, however, to th ink seriously about developing such beams and indeed special accelerators, largely or even

solely for the purposes of nuclear s t ructure research. I t is therefore appropriate to examine the sort of information one can hope to gain about the nucleus

* A lecture delivered in Budapest on 25th October 1965 to the Hungarian Physica] Society.

Acta Ph)sica Academiae Scientiarum Hungaricae 21, 1966

25~ D . H . WILKINSON

through the medium of elementary particles and to assess whether it is sufficiently important and sufficiently novel to justify the very considerable expenditure tllat this forro of experimentation will entail. I shall not attempt, in this lecture, to shoulder the responsibility of recommending for or against such expenditure. I aro in no way attempting a synoptic aecount of the subject - - great areas will be left untouehed: I shall, for example, omit nucleons and electrons completely. Still less aro I writing a proposal f o r a meson factory -- that document would look very different from this lecture. But I shall t ry to show by a few eclectic examples: (a) that we have already benefitted in our knowledge of nuclear structure from the use of elementary particles; (b) that there is a wealth of important nuclear structure information to which elementary particles might lead us in the future; (c) that care is going to be needed in interpreting the results. I shall have to strike some sort of balance of empha- sis between (a), (b) and (c); I shall hope to do this fairly but I should also say that (c) would have had to loom large in some of the topics I have omitted had time allowed their inclusion.

The e o m p o s i t i o n o f the nuc l ear sur face

Before examining, particle by particle, the type of nuclear structure information that we might obtain, ir may be interesting to illustrate the knowledge about the nucleus tha t has already been gained through elementary particle probes by reference to a single problem. This will, I hope, eonvince you that use can be, and already has been, made of elementary partieles for giving us information that ir would be very difficult to get by conventional means. The problem is the composition of the nuclear surface: is the nuclear surface composed chiefly of neutrons or chiefly of protons or is it composed of neutrons and protons in more or less the same N : Z proportion as for the nucleus a s a whole ?

Tbis is obviously a very important question for nuclear structure; that ir is ah open question may be shown by two simple contradictory arguments. The first of these is that the protons in the nucleus are positively charged while the neutrons are neutral; the protons therefore repel each other which the neutrons do not and so tend to get as far apart as possible making the edge of the nucleus proton-rich. The second argument is a little more complicated and is illustrated in Figure 1. This Figure shows the potential felt by a neutron as ir enters the nucleus and also the potential felt by a proton. Owing to the charge independence of the specifically-nuclear force, the proton potential differs from the neutron potential essentially by the addition of the repulsive Coulomb force which lifts up the proton potential and makes it, as shown, not so deep as the neutron potential inside the nucleus. The nucleus may then be thought

.4cta Physica ~lcademiae Scien;iarum Hungaricae 21, 1966

A. FEW USES OF ELEMENTARY PARTICLES 257

of, crudely, as bui l t up by siting neut rons and protons in the i r respective potentials up to a cer ta in level t ha t represents the binding energies. This level must be more-or-less the same for neut rons and for protons, otherwise be ta -decay will conver t one into the other unti l equil ibrium is reached. As may be seen f rom the Figure, owing to the sloping sides of the nuclear potent ia l this means tha t the protons ate confined by ah effect ively nar rower potent ial than the neut rons and so the edge of the nucleus must be neutron-r ich.

These two con t r a ry arguments are bo th false bu t are also both superficially plausible. T h e y at least suffice to show tha t the quest ion about the composit ion of the nuclear surface does not have a simple common-sense answer. Nor is ah answer given b y the most sophist icated analysis t h a t we

Proton~ ~ Neufron po,~enha/

Fig. i

ate ye t able to make ; ah exper imenta l answer is clearly demanded to provide a bounda ry condi t ion for fur ther speculat ion about nuclear s t ructure .

To some degree, the convent ional methods of nuclear s t ruc ture experi- menta t ion ate sensitive to the neut ron-versus-pro ton rat io in the nuclear surface, for example relat ive nucleon reduced widths are clearly dependent on the relat ive nucleon distr ibution. However , the ex t rac t ion of such widtbs f rom exper imenta l da ta is a delicate and b y no means unambiguous procedure and demands full fa i th in the Dis tor ted Wave Born Approx imat ion on which one knows one cannot re ly for real ly quan t i t a t ive answers. One is therefore led to seek a comple te ly new approach. The use of e lementa ry part icle probes has provided three such approaches which will now be br ief ly summarized.

(i) ~+ v e r s u s 7 t - c r o s s - s e c t i o n s

General ly speaking the nucleon cross-section for the collision of a particular charge of pion will be different for neutrons and for protons. Charge independence then provides:

( l~+p ~ ff:,--n =/= O'~+n = O ' ~ _ p .

Imagine now, for the sake of a rgument , t ha t we could f ind a pion energy at which the above inequal i ty sign reads " v e r y much smaller t h a n " . Imagine

Acta Physica Academiae Scientiarum Hungaricae 21, 1966

255 D . H . WILKINSON

also that the nucleus has, in fact, a neutron-rich surface so that the "neutron nucleus" is bigger than the "proton nucleus". In this case bombardment of the nucleus with positive pions will see chiefly the neutron nucleus while bombardment with negative pions will see chiefly the proton nucleus. Since the neutron nucleus is bigger than the protou nucleus the cross-section for positive pions wiI1 be bigger thau that for negative pions. In fact, a t a pion energy of about 700 MeV a~_p is more than twice as b i ga s a=+p. Under these circumstances calculation shows a 6 to 8% differencein (a~_ -- a.+)/a.+ for a heavy nucleus depending on whether the neutrons and protons occupy the same region of space or whether there is a neutron-rich surface such as would correspond to the central density being the same for neutrons and protons. I t is now 10 years since the theory was worked out [1] and the experiments performed [2] showing that , within experimental accuracy, the neutron and proton distribu- tions have the same radius and there is no significant skin of either type of nucleon on the surface.

(ii) Elastic neutral pion photoproduction

We know quite well the distribution of protons in the nucleus froIn the elastic scattering of high-energy electrons, particularly the work of HOFSTADTER at Stanford. We have, however, rather little information on the distribution of mat ter in the nucleus, tha t is to say, neutrons and protons without regard to their charge. A nuclear reaction that does not basically distinguish between ncutrons and protons is the photoproduction of neutral pions. Ir this is carried out elastically from a complex nucleus, that is to say, leaving the target nucleus in its ground state, then the process is a coherent one aud the angular distribution of the resuhant neutral pions represents the coherent superposition of the production amplitudes from all the individual nucleons; the angular distribution therefore depends, in the usual way of a diffraction pattern, on the spatial distribution of the nucleons. Careful measurement of this angular distribution then gives information about the mat ter distribution. These experiments have been done [3] and show an essentially-identical distribution for the mat ter as for the protons revealed through elastic electron scattering: there is no marked preponderance of either type of nucleon on the surface.

(iii) Absorption of K--mesons

When a negatively-charged particle is slowed down in matter it eventually falls under the influence of a particular atom and spirals in towards the nucleuss passing through a very large number of quantum orbits and proceeding inwarde by a eombinatiou of Auger and radiative transitions. At first the Auger process will be the stronger but later radiative transitions will take over. At this stag,


A FEW USES OF ELEMENTARY PARTICLES 2 5 9

we should expect the orbits, semi-classically speaking, to become more and more circular because at each stage of the radiat ive process there will be a t endency to make the t ransi t ion to the s ta te of highest s tat is t ical weight, namely t ha t of highest allowed /-value. I t is ant ic ipated t h a t the orbits will become circular before the nucleus is closely approached and so the final capture will t ake place from states of I -~ n - - 1. In the case of K - - m e s o n s , the absorpt ion is so ve ry strong t ha t one m a y easily ealculate tha t the absorpt ion will, in fact , take place at the edge of the nucleus where the nucleon densi ty is low [4]. This region we might t e rm the "nuc lear s t ra tosphere" . The absorp- t ion products therefore bring us informat ion about the composi t ion of this s t ratosphere. The absorpt ion of K-mesons on single nucleons goes by the following processes:

K - + p--~ X - + ~t +

Zo + zeo

~ + 21- T �91

A o + ~zo

K § n - - , - Z - + z *

S o + ~ -

AO+~e -

We see tha t , a l though absorpt ion on protons can lead e i ther to L "+ or to Z -

absorpt ion on neut rons cannot make 27 + bu t of the charged Z-hyperons only2?-. The product ion of 27+ in K - - m e s o n absorpt ion therefore signals the presence of protons in the nuclear s t ra tosphere. In te rp re ta t ion of the exper iments is still somewhat complicated by our lack of complete knowledge of the element- a ry part icle constants involved, but , so far as we can see at the moment , the results are comple te ly consistent with there being the same N : Z mix ture of neutrons and protons in the s t ra tosphere as there is in the depths of the n u c l e u s .

These three e lementary-par t ic le approaches to this quest ion aro to ta l ly different the one f rom the other bu t all agree on the answer, namely tha t the nuclear surface is not not iceably r icher in one sort of nucleon t h an the other and is most p robab ly of about the same composi t ion as average nuclear mat ter . This is a l ready something of considerable nuclear s t ruc ture interest tha t we know about essentially only f rom the e lementary-par t ic le exper iments .

We will now look sys temat ica l ly bu t far f rom exhaus t ive ly at some kinds of informat ion t ha t some of the various e lementa ry particles can bring us about nuclear s t rueture .

g Acta Physica Academiae Scientiarum Hurtgarieae 21, 1966

260 D. H. WILK1NSON

Muons

The muon is a magnif icent probe for the nucleus because it is so weakly coupled to the nucleon field. In t e rp re t a t ion of the g - - 2 exper iments on the muon show tha t G2/4~r < 10-3. We can therefore neglect the nuclear in te rac t ion of the muon complete ly b y comparison wi th its electric interact ion. In this respect the muon is just like ah electron bu t its greater mass brings ir cer ta in advantages .

Muonic atoms: nuclear charge distribution

The dis tr ibut ion of charge within the nucleus is a m a t t e r of intense interest . At the momen t our chief knowledge about this comes f rom the elastic scat ter ing of energetic electrons bu t the energies of muonie X-rays are also, in principle, capable of tell ing us a lot about the charge distr ibution. Because the muon is 200 t imes heavier t han the electron its orbi t is p ropor t iona l ly smaller and m a y be comparable with the size of the nucleus. The electrie field within which it moves cannot t hen be taken as t h a t of a point charge; the f inite size of the nucleus is significant and there is a level shift from the value calculated f o r a point nucleus.

In the first approx imat ion one t reats the ent ire nuclear size as a per turb- ation, f inding a level shift for the muonic a tom of:

2~r ~ E = Z ~ ~ k~(0)l -~ <r2>.

3

Here ~(0) is the SchrSdinger point-nucleus solut ion for the muon 's wavefunct ion. In this approx imat ion the exper iments tell us only <r2> which does not pu t t hem into eompet i t ion with electron scat ter ing which is a l ready sensitive to t w o p a r a m e t e r s t ha t measure the radius and the surfaee thiekness.

To invest igate the po ten t ia l i ty of the muonic X- ray me thod in more detail we mus t make an exact solution of the m u o n wavefunet ion in wha teve r charge distr ibution we care to investigate. The classical charge dis t r ibut ion for such purposes is the FERMI or SAXON--WOODS form:

e( r ) ~-~ [e ( r -R) ' " + 1 ] - 1 .

For this forro of dis t r ibut ion for Pb using the values of R and a deriving f rom electron scat ter ing a 10% change in the radial pa rame te r R changes the energy of the 2p3/2 to lsl/2 t rans i t ion by 8 , 2 ~ . Similarly a 1 0 ~ change in the surface thickness pa rame te r a changes the same t ransi t ion energy b y 1 , 1 ~ .

We must now pause and ask ourselves how accura te ly can we hope to measure these muonic X - r a y energies. Given suff ieient ly-intense beatos of

Acta Physica Acaderniae Scientiarura Hungarieae 21, 1966

A FEW USES OF ELEMENTARY PARTICLES 261

stopping muons we can apply ei ther crys ta l spec t rometer methods or Ge(Li) counter methods . These methods offer us ah u l t imate aecuracy of perhaps 0,1 ke u for the X - r a y energies involved provided t h a t the problem of calibration can be solved. I t superficially appears, then, tha t the dis t r ibut ion parameters can be de te rmined wi th enormous accuracy sinee the t ransi t ion energies in question in the heavier elements ate of the order of 6 MeV. This, however, is wholly i l lusory because we must de termine bo th parameters at the same t ime and not assume t h a t one of them is known a priori. In faet we ate immedia te ly led to ask whether we should not in t roduce a th i rd pa rame te r into our descrip- tion of the charge distr ibution. The electron-scat ter ing exper iments ate jus t beginning to become sensitive to a possible th i rd pa rame te r and so if the muonic X- ray work is to be compet i t ive with the electron scat ter ing it too must demons t ra te a sensit ivi ty to a th i rd parameter . Consider the forro:

o(r) ~-~ [1 + ~r2]/[e 'r-R) a + 1].

We will invest igate the following reasonable ranges for the three parameters : a : (0,5 to 1,5) F ; R : (1,0 to 1,2) A l~a F ; cr : (0 to 1,25) (A V3 F) -2. This form of charge dis tr ibut ion is taken to represent the t endency in a h eav y nucleus for the mutua l Coulomb repulsion of the protons to have some effect. Within these pa rame te r ranges the energy for the 2p3, 2 to lsl/2 t rans i t ion in Pb m ay ehange b y as m u c h a s 1 MeV. Consider f i rs t the 2pa,2 to lsl/2 t ransi t ion. Is this t ransi t ion energy were known preeisely then the whole range of var ia t ion of the parameters in the above expression would eorrespond to var ia t ions in the energy of o ther t ransi t ions by a few tens of keV. Ir, in addi t ion, we knew the 3d5/o to 2p3/2 t ransi t ion energy precisely, then the above p a r am e te r range corresponds to a var ia t ion in energy of the 2sl/2 to 2p3/2 t ransi t ion by about 2 keV [5]. Since we are hypothesiz ing an accuracy of 0.1 keV we see tha t , in principle, ir m a y be possible to make a th ree -paramete r de te rmina t ion to an accuracy of several percent on each of the three parameters . This would, of course, be ex t remely valuable a l though we must not forget the arbitrariness in the choice of the aspects of the charge dis tr ibut ion t h a t we choose to para- meterize. This corresponds to some doub t as to the relat ionship between our inferred dis t r ibut ion and physical rea l i ty and emphasizes the desirabil i ty of having available complemen ta ry approaches of comparable sensi t iv i ty -- muonic X-rays and electron seat ter ing in the present example.

Even before we doubt the relevance of the analysis to the real world we must examine cri t ically various factors t ha t might dis turb the analysis. We have assumed t ha t the problem is exac t ly described by the solution of the Dirac equat ion in the field of a s t ruc tured bu t inert and unresponding nucleus. Both these assumptions must be quest ioned. As to the f irs t one, our present level of unders tanding suggests t ha t all we need to do is to allow for vacuum

4 * Acta Physica Academiae Scientiar~~rn Hungaricae 21, 1966

2'~2 D. H. WILKINSON

polar izat ion; al though this correct ion eonsiderably exceeds the 0,1 keV of our assumed accuracy of measurement , ir is well unders tood and we will t ake ir t h a t the correct ion can be made sufficiently exac t ly not to disturb the analysis as we have presented i t so far.

A more serious diff ieul ty is represented b y the assumption t h a t the nucleus is iner t , is unaffeeted b y f inding i tself in the electric field of the muon. This is obviously not correct and we must es t imate , using second order per- tu rba t ion theory , the shift in the muonic energy levels to be associated with exci ta t ion of the nucleus into and out of all possible vi r tual states. In o ther words, we must evaluate the shift:

~IE, = ~ ' <T0~k {HI T=~~><~=~~ [HI ~0~k> B J~ (Eo -4- Ek - - E . -- E~)

n, i~ are the in termedia te nuclear and mesonic states; ~Y and ~ ate the nuclear and muonic wavefunct ions; H is the muon-nucleus in teract ion Hamil tonian . Present calculations of this polar izat ion shift for the 1si! 2 level in Pb range from 58 keV to 8,2 keV [6]. While the reason for this large range of theoret ical resuh is unders tood in terms of the different sorts of approximat ion involved in the different calculations the fact t ha t the correct ion is so enormously greater t han the accuracy with which we have imagined the measurements can be made and in terpre ted is v e r y worrying. I i is not at the momen t clear what can be done about this problem. Of course, i t m a y be possible to tackle it to some degree semi-empirically by comparison of neighbouring elements, neighbouring transi t ions, and so on, bu t ir is clear t h a t it introduces a considerable complicat ion into our a t t empt s to ex t rac t a th i rd pa ramete r of the charge dis t r ibut ion by these methods . We m a y even be t e m p t e d to inver t the process: say t ha t we know sufficient about the charge dis t r ibut ion from the electron scat ter ing measurements to use the muonic X - r a y da ta for telling us something about nuclear polarization. I t would indeed be interes t ing to know ir there is any sys temat ic dependence of nuclear polar izabi l i ty on various parameters such as nearness to closed shells, deformat ion and so on.

Quadrupole effects

Other effects disturb the simple analysis bu t also bring us in format ion of impor tance in their own right .

Consider quadrupole effects. In ordinary atoms the quadrupole spli t t ing is seen a s a per turba t ion of the magnetic hyperf ine s tructure. In the case of muonic a toms the quadrupole effect dominates. This is because the rat io of the quadrupole effect to the hyperf ine spli t t ing is approximate ly : [e2Q,/r3]/[~~,/r 3] which has the value of about 200 for muons as against approx-

Aeta Physica Ar Seientiarum Hungaricae 21, 1966


imately un i ty for electrons because the muon 's magnet ic momen t is about 200 times less t h a n the electron's. In the case of muonic X-rays we have, therefore, the oppor tun i ty to gain informat ion about the nuclear quadrupole moment with a directness tha t is denied us for electrons. I r we consider the 2p to l s t ransi t ions we should, in general, i f the nuclear spin allows it, f ind not the two transi t ions 2p3, 2 to 181,2 and 2pl:z to ]st/2 t h a t arise i f we neglect the quadrupole momen t bu t ra the r f ive, f rom which the quadrupole momen t may be ex t rae ted .

Ah interest ing effect comes about owing to the coupling between the muon and the nucleus. This coupling implies t h a t ir is possible, in the course of the X- r a y cascade, for the muon ac tua l ly to excite the nucleus into a real excited state. This will be par t icular ly l ikely in the heavy elements which have

~r~ I [ t. I -200 0 200 400

A"EV

Fig. 2

low-lying ro ta t ion states with large E2 transi t ion moments and excitat ions comparable with the 2p:~ 2 -- 2Pt/2 splitt ing. This means tha t the five lines expected ir this effect is neglected will become ten, f ive of which are associated with the real exc i ta t ion of the nucleus. I t turns out t ha t the nuclear t ransi t ion s trengths and spacings ate such t ha t in certain heavy nuclei these two groups of five transi t ions m a y be of comparable intensi ty. Since this exci ta t ion can come about in a nucleus whieh has J----- 0 in its ground state, we are able to measure quadrupole moments in nuclei t ha t do not normal ly permi t of sueh a measurement .

Ah impor t an t and exciting point is t ha t the distr ibution of the quadrupole split t ing is sensitive to the sign of the quadrupole m o m en t and not jus t to its magni tude. This is i l lustrated in Figure 2 which shows approximate ly the distr ibution and relat ive s t rength of the quadrupole-spl i t t ransi t ions calculated for T h 232 o n the two assumptions: t ha t the nucleus is prola te and tha t it is oblate. As m a y be seen the pa t te rns for the two signs ate ve ry different and so comparison with exper iment reveals the sign of the quadrupole moment which ir is ex t remely difficult to determine by any other t ype of exper iment . This in i tself m a y be a ma t t e r of considerable impor tance and jus t i fy considerable effort in the measuring of muonic X-rays.

Acta Physica Academiae Scientiarttm Htt,'tgaricae 21, 196£

264 D. H. WILKINSON

Magnetic splitting

The magnet ic spl i t t ing is usual ly m u c h smal ler t han the quadrupole

spl i t t ing for muonic a toms b u t in the lSl/2 s t a te of h e a v y a toms the magne t i e spl i t t ing m a y be as big as 1 to 5 keV with no eompl ica t ions f rom quadrupole spl i t t ing. This magnet ic spl i t t ing should be measurab le . I f all t h a t i t to ld us were the magne t ic m o m e n t of the nucleus there would be noth ing to be exci ted

about . However , in the b e a v y e lements the 1sl/2 s t a te lies to a large degree inside the nucleus so the magne t i c spl i t t ing is de te rmined not b y the overall magne t ic m o m e n t bu t involves the distribution of magne t i c m o m e n t wi th in the nucleus. This again is someth ing t ha t is e x t r e m e l y diff icuh to get a t b y convent iona l means and so there m a y be here also a considerable field for

exploi t ing muons. We m a y note in passing t h a t it is in principle possible to make these

magne t ic measu remen t s on the par t ic le -bound exci ted s ta tes ofnucle i b y resonant sca t te r ing of muons [7]. There is ah elastic sca t te r ing process in which the inc ident muon is c ap t u r ed into its lsl/2 orbi t wi th aceompany ing exc i ta t ion of the nucleus into a defini te s ta te followed b y eject ion f rom the orbi t and s i m u h a n e o u s de-exci ta t ion of the nucleus. This will be a resonant process of large cross section (~~r ~2) b u t v e r y small wid th ; i t will show the magne t i c hyper f ine spl i t t ing due to the magne t i c m o m e n t of the exci ted nuclear s ta te : there wiI1 no t be one resonance for each exci ted s t a te b u t r a the r two, correspond ing to the two or ien ta t ions of the muon spin re la t ive to t h a t of the nucleus. This hyper f ine spl i t t ing is t hen a measure of the d is t r ibut ion of magne t i c m o m e n t in the excited s t a te of the nucleus, h is not clear whether such measu- r emen t s will ever be feasible in prac t ice bu t in principle they open up ano the r great and i m p o r t a n t field.

Nuclear diamagnetism

We m a y finally note the possibil i ty of measur ing nuclear d iamagne t i sm using muons [7]. h will obv ious ly be mos t in teres t ing for nuclear s t ruc ture work to know quan t i t a t i ve l y the degree to which the nucleus is d iamagnet ic . Dimens iona l ly we m a y expec t an induced magne t i c m o m e n t of abou t 10 -17 H nuclear magne tons in a field of H gauss. For Z = 20 one nuclear m a g n e t o n in the nucleus corresponds to a field of abou t 10 x3 gauss at the m u o n orbit . Therefore a t the m u o n orbi t , owing to the nuclear d iamagne t i sm, we m a y expec t a field of abou t 10 -4 H gauss. This m a y be a ju s t -measurab le effect on the m u o n ' s precession f requency . This effect increases rap id ly wi th Z. Again we m a y note t h a t in principle we are sensi t ive to the spat ia l d is t r ibut ion

of the induced d iamagnet ic m o m e n t .

Acta Physiea A�91162 Scientiarura Hungaricae 21, 1966


Muon capture

The cap tu re of negat ive muons b y the nucleus is a weak in te rac t ion and is sensit ive to the details of the nuclear wavefunct ion . At the m o m e n t , this process is too m u c h bedevil led b y our uncer ta int ies abou t the basie muon cap ture process i t se l f to begin to use ir seriously as a tool for p rob ing nuclear s t ructure . We are still in the stage of using nuclei whose proper t ies we believe we unde r s t and fa i r ly well to learn abou t the m u o n and its in teraet ions . When these a te suff ic ient ly well unders tood the process can be reversed and can in principle yield i m p o r t a n t informat ion . I n cer tain l imited cases useful informa- t ion could be had a l ready if suff icient ly intense muon sources were available. For example , the react ion d -}- # - --~ 2n -}- r wi th s imul taneous energy and angle m e a s u r e m e n t on bo th neut rons would bring va luable in fo rmat ion abou t the nn in teract ion.

Inelastic scattering

Muons m a y also be useful for more convent ional types of exper iment . For example , m u o n inelastic sca t te r ing will be ve ry m u c h like electron inelastic scat ter ing and will be valuable in br inging us in fo rmat ion abou t nuclear wavefunct ions and m a t r i x elements. In this muons have the a d v a n t a g e over elec- t rons t h a t thei r b remss t r ah lung is v e r y m u c h less; this will m a k e possible cer- ta in types of inves t iga t ion closed to electrons. Another technical advan tage is t h a t muons have more m o m e n t u m for a given energy t h a n electrons and so be t t e r energy resolut ion is avai lable for a given m o m e n t u m transfer . Muons are c o m p l e m e n t a r y to electrons in inelastic sca t te r ing exper iments in t ha t they explore different regions of ene rgy - lo s s -momen tum- t r ans fe r space.

Pions

The pion is the q u a n t u m of the nuclear force field, or a t leas t of its tail, and so migh t be expec ted to be of direct re levanee to the p rob lem of nuclear s t ructure . This, however , is not so, a t leas t for this decade, bu t i t is still ve rv va luable as spinless, s t rongly- in te rac t ing T = 1 energy.

Elastic scattering

Lit t le seems l ikely to come in the i m m e d i a t e fu ture f rom elastic scat ter ing optical model s tudies in the way of nuclear s t ruc ture in format ion . Confronta- t ion with ealculat ion based on the empir ical pion-nucleon in te rac t ion is obviously in teres t ing in its own r ight and is in principle ah approach to correlat ion

Acta Physica Academiae Scientiarum Hungarieae 21, 1966

266 L ~/. WILKINSON

effects. Thcre are, however, many complications; the way is only now bccoming elear for a programme with the specific objective of tel]ing us about nuclear structure.

Pionic atoms: nucleon-nucleon correlations

A matter closely related to elastic scattering tha t does hold more imme- diate promise of yielding important data is the study of pionic atoms. By stu- dying the pionic X-rays we can measure directly the width and infer the shift of the ls-level and can infer the shift of the 2p-level. Indirectly (from the X~ intensities) we can determine the 2p- and 3d-widths. These shifts are due to the attraction of repulsion exerted on the pion by the nucleus and the widths ate due to the absorption of the pion by the nucleus. We can compare the inferred magnitude of the force and the absorption with what we expect on the basis of various empirical pion-nucleon interactions and so infer something about the condition of the nucleons instale the nucleus, particularly their correlations.

To do this we must obviously have a theory tha t predicts the pion- nucleus optical model potential in terms of ~N and ~zNN free space interactions. This theory is very difficult to make and ir has not yet been done unambiguously. We may illustrate the way in which the calculation might go from the work of EmcsoN and ERICSO~ [8]. The potential importance of pionic X-ray studies for giving us information about nuclear structure does not depend on the detailed correctness of this particular calculation; here we just use i t a s ah illustration of the degree of sensitivity that the experiments might have to certain details of the nuclear wavefunction. EmcsoN and ERICSON first of all derive that part of the optical model potential that is due to the multiple scattering of the pion on single nucleons; i.e. coming from the ~N interaction. They write down the multiple scattering equations, truncate at the pair correlations and find in the nonrelativistic limit:

V(r) -- --4~rh2 [ be(r ) -- ~. ce(r) ~ ] 4zc 2/x [ 1 ~_ ~ ce(r ) J

(This derivation assumes very short range correlations and negligible nuclear excitation energies.) The first term in this expression is a local potential that arises from the s-wave ~N interaction. The second term is non-local of velocity dependent and comes from the p-wave ~N interaction which for low energy pions is strong and attractive (the (3,3) resonance at a bombarding pion energy of about 200 MeV) as against the weak and repulsive s-wave ~N interaction. The nonlinearity of the second term depends on the correlations and is the analogue of the LORENTZ--LORENTZ effeet (the n~nlinear dependenee of refrac-

.lcta Physica Academiae Scier~iarum Hungaricae 2], 1966

& FEW USES OF ELEbiENTARY P&RTICLES 267

t i re index on density for light passing through a dense homogeneous medium of pola¡ atoms); as ERICSON and EmCSON have picturesquely pointed out, a low energy pion behaves somewhat like a strongly interacting photon. We must also consider the explicitly-two-nucleon scattering amplitude, coming from the ~NNinteract ion, which contains terms such as { B + C ki �9 kf + . . . } (the ks are the initial and final pion momenta). Here again the first term is local, coming from s-waves, and the second is non-local, coming from p-waves. The overall local interaction (which includes both the ~N and the ~ N N terms) is determined to be, as expected, repulsive, from the ls-shift. The

o,3

0,2

C

o,1

0 0

No correlofion~

0.05 O1 /mg

Fig. 3

2p-shift shows ah attractive force and with the local interaction already determined by the ls-shift, enables us to get a measure of the non-local interaction. The widths are due to absorption and so determine the imaginary parts of the two-nucleon amplitudes (the contribution to absorption from the one-nucleon terms is negligible). The ls-width determines I m B . The 2p- and 3d-widths thš give ImC. These quantities may now be comp ared with expectation based on the free ~N scattering cross sections and information about the ~ N N interaction deriving from reactions such as:

p + p _ _ _ ~ s t + + d ; p + p . _ + ~ O + p + p .

The calculated values of the shifts and wi dths obviously depend on the assumptions made about the nucleon-nucleon correlation inside the nucleus. Fig. 3 shows the comparison between the expectation based on the ~N and ~ N N interactions both with and without a degree of nucleon-nucleon correlation inside the nucleus such as would correspond to the effect of the conventional hard core of the nucleon-nucleon interaction. Ir is seen tha t better agreement is obtained on the assumption of the reasonable short-range anti-correlation than for ah uncorrelated nuclear wavefunction.

Acta'Physica Ac,td,,miae Scientiarum Hungaricae 21, 1956

2• D. H. WILKIiNSOI~I

As was remarked earlier, we cannot in te rpre t these exper iments at the momen t as proving the existence, inside the nueleus, of the expected nucleon- uucleon correlat ion beeause the theory is not ye t free of ambiguities; the experiments are also ra ther crude. The purpose of the present comparison is to i l lustrate the sensit ivi ty of the measurements to the nuclear-s t ructure paramete r of interest . I t is clear t ha t impor tan t in format ion can be got f rom a more detai led exper imenta l and theoret ieal s tudy of pionic atoms.

Nuclear absorption

Another use tha t has a l ready been made of pions and tha t can be con- s iderably ex tended is the stucly of the details of the i r absorption b y nuclei. Consider absorpt ion of negat ive pions at test . The pion brings a considerable amoun t of energy (about 140 MeV) into the nucleus on absorpt ion bu t negligible mome n tum . The energy is u l t imate ly t r ansmi t t ed to nucleons which mus t therefore leave the nucleus wi th considerable energy and momen tum. Since the pion provides no m o m e n t u m the m o m e n t u m must come f rom the interaction of the nucleons with each other, e i ther in the initial or the final s tate . Since the mom en tum involved is considerably higher than the Fermi moment - um inside the nucleus, we should expect single nucleon absorption, in which the recoil is essentially t aken up by the optical model potent ia l of the rest of the nucleus, to be ra the r unl ikely and the commones t event to be one of absorpt ion on a closely-correlated nucleon-nucleon pair ; the final s ta te moment - um then derives f rom the nucleon-nucleon r a the r t han from the nucleon- nucleus interact ion. In this case nucleons should emerge from such absorpt ion events in pairs correlated ve ry roughly at 180 ~ to each other. I f the nucleus is l ight it is quite likely t h a t bo th members of the nucleon pair will emerge and will ca r ry with them a fair ly good mem o ry of the m o m e n t u m state associated wi th the p r imary absorpt ion process. In heavier nuclei final s ta te interactions of the nucleons with the rest of the nucleus on the way out will become impor t an t and ir will be more difficult to derive informat ion about the p r im a ry absorpt ion process f rom the final products . Such nucleon pairs, with the expected s t rong ant icorrelat ion, have been known for some considerable t ime [9] bu t have more recent ly been studied in greater detail. Their angular correlat ion, if the final s tate in terac t ion can be unders tood, will gire informat ion about the m o m e n t u m distr ibution of the absorbing pair i tself inside the nucleus and this in tu rn is ah impor tan t pa ramete r , related, for example, to the degree of three- part icle clustering.

W h a t do we learn f rom the na ture of the emergent nucleon pa i r s? The negat ive pion may be absorbed either by a pair of protons of by a neut ron- p ro ton pair. In the first case wha t we see emerge is a fast ant icorrelated neutron- p ro ton pair and in the second case a similar neu t ron-neu t ron pair. Off-hand we should expec t there to be something like four t imes as m an y neu t ron-neu t ron

Acta Ph.ysica Academiae Seientiarum Hungaricae 21, 1966


f inal-state pairs as neu t ron-pro ton f inal-s ta te pairs. This is because the captur ing neu t ron-p ro ton pair may be in e i ther a t r iplet of a singlet s ta te whereas the captur ing p ro ton-p ro ton pair must be in a singlet s tate . This assumes t h a t the chief N N states operat ive in the nucleus ate s-states following the observed feebleness of the p - s t a t e in teract ion in free N N collisions. If, however, the p-s ta te in terac t ion were strong inside the nucleus, then the neu t ron-pro ton f inal-state pairs would be relat ively boosted because the s ta t is t ical ly-weighty tr iplet p -s ta te would then be admi t t ed for the initial p ro ton-pro ton interact ion. The possibil i ty t h a t the effeetive residual nucleon-nucleon in teract ion inside the nucleus is s ignif icantly different f rom the free nueleon-nucleon interact ion is ah ex t remely i m p o r t a n t and open nuclear s t ruc ture quest ion. We should therefore be ve ry eager to pursue any invest igat ion, such as the one now being discussed, which promises to bring us news about the nucleon-nucleon interaction inside nuclear mat te r .

In fact exper iments show an excess of neu t ron-neu t ron f inal-state pairs over the number expeeted by mete counting. This m ay superf icial ly appear to suggest t ha t the t r ip le t s-state in teract ion, operat ive only for neu t ron-pro ton absorbing pairs, is s t ronger at the distances of about 0,5 F re levant for this absorpt ion process t han the singlet s-state interact ion. This would be ah import - ant conclusion. However , we have here an example of the caut ion tha t mus t be exercised in in te rpre t ing the resuhs of e lementary-par t ic le-nucleus interaction exper iments . The point is tha t the simple expec ta t ion t h a t we have jus t described is based on the assumption t ha t the pion is absorbed by tha t nucleon of the correlated pair with which it f irst interacts . We must , however, recognize the possibility t ha t rescat ter ing may be impor tan t : the pion scat ters off the first nucleon of the correlated pair and is absorbed by the seeond. There ate m a ny diagrams t ha t cont r ibute to this type of high order process, This process m a y come about most simply, however , th rough a q)~ or q~q~ te rm in the Ha- mil tonian (where q~ represents the meson field and ~t is the conjugate field operator). Tha t is to say, the initial in terac t ion m ay be 'seat tering wi thout of with charge exchange. This rescat ter ing mechanism would boost the t r iplet s-state absorpt ion relat ive to the singlet s-state absorpt ion because charge exchange contr ibutes to the former bu t not to the la t ter . We therefore here have an altern- a t ive reason why the f inal-s ta te neu t ron-neu t ron pairs are more abundan t relati- ve to the f inal-state nleutron-proton pairs t han we f ind by mere counting, and in this case we are learning nothing about the relat ive s trengths at short distanees of the NNin t e r a c t i ons . In fact the rough magni tude of the rescat ter ing pheno- menon m a y be es t imated using informat ion from the p + p -+ ~+ + d and p + p _+ p + p + ~o reactions near threshold and appears to be of about the r ight size to explain the exper imenta l ~ - - c a p t u r e data.

We must obviously be careful about making a too-naive in te rpre ta t ion of exper iments of this kind.


2 7 0 D, i i .WILKINSOiN

Other correlations

We have ment ioned the use of negat ive-pion absorpt ion to look for np and pp correlations. I t will be also interest ing to use finite b u t low-energy posit ive pions in reactions such as (zr +, np) and (zr +, pp) to supplement the in format ion coming from the negative-pion absorpt ion at test.

We m a y f inal ly note the possibility of using pion absorpt ion to look for three-nucleon correlations with clusters such as:

~r+ -~ npp--~ 3 p ,

~r- § ppp---~ n ~- 2p.

Pion production

Other possible uses of pions are legion: for example the react ion

p-l- --~ @ ~r + for large momentum t ransfer is sensitive to the

nueleon-nucleon correlat ion inside the nucleus and impor t an t informat ion

�9 / ~ + ' l will be for thcoming par t icular ly when the residual nucleus Z is left in

ah ident if ied state. Pion produc t ion from a complex nucleus below its threshold for free N N collisions will also tend to show up high m o m e n t u m states in the t a rge t nucleus wavefunct ion (this is t rue of any product ion process).

Inelastic scattering

Pions possess certain advantages for s t ra ight forward inelastic scat ter ing work in t ha t they are spinless and are distinguishable f rom nucleons. Since pions ate of T =- 1 they can excite transi t ions of A T = 2 and so m a y show up new forms of collective mot ion and can reach states difficult of access b y other methods. (zr, ~ry) react ions may have certain advantages for wavefunc- t ion studies over the corresponding nucleon-induced reactions since there is no spinflip possible for the bombard ing pion.

Double charge exchange

The charge-exchange possibilities with pions also open up interest ing fields. Of par t icular interest m a y be the double charge exchange react ions: (zr -+, zt;). Wi th low energy pions we will t end to excite low-lying analogue states. I t is not at the momen t clear what nuclear s t ruc ture informat ion m a y be obta ined from this a l though i t will be interest ing to look for the T �9 ~ t e rm in the pion-nucleus potential . I t will be interest ing to discover whether the double charge exchange is to be associated with an isotopic tensor t e rm in a two-nucleon effect of with the repeated applicat ion of the isotopic vec tor

Acta Physica Academiae SeientiartJm Hungaricae 2J, 1966

A FEW USES OF ELEMENTARY PARTICLES 2 7 |

term. Such reactions should give information about nucleon-nucleon correlations if they can be interpreted unambiguously.

A further possibly-interesting use for pion double charge exchange is to reach systems that are otherwise very difficult to study. Some examples ate:

Hea (~-, ~+) 3n, He 4 (~-, x+) 4n ,

Ha (~+, ~-) 3p, Li 7 (3t-, zt +) H 7 .

lntrinsic nucleon magnetic moments

We have already discussed the elastic photoproduction of neutral pions as ah approach to the problem of the mat ter distribution within the nucleus. Other sorts of photoproduction may also, in principle, yield valuable information. Much information of importance for nuclear structure is locked up in the many very accurate values of nuclear magnetic moments tha t we now possess. Unfortunately interpretation of these accurate data is bedevilled by our ignorance of the degree to which the mesonic exchange currents within the nucleus that are responsible for the nucleon binding concomitantly modify the nucleon intrinsic magnetic moments. I t is elear tha t some such modification must take place, but it is unclear how important this effect may be. I t is very difficult to disentangle this modification of the intrinsic magnetic moments from the detailed effects of the nuclear wavefunetion tha t we want to use the overall magnetic moment to probe, partieularly when one must recognize the likely importance of considerable amounts of two-particle-two-hole excitation and other forros of configuration interaction. An experiment tha t bote directly on the question of the nucleon intrinsic magnetic moments inside the nucleus would be extremely valuable. In principle, one can approach this problem through pion photoproduction since the reaction ? -~ N ~ ~ ~- N involves directly the intrinsic nucleon magnetic moments [11]. I f we may treat pion photoproduction from a complex nucleus in the impulse approximation, if it is from single nucleons and if we may neglect the importance of final state interactions, then a comparison of tha t photproduction, particularly the nucleon polarization with the corresponding reaction on free nucleons gives us a measure of the desired nucleon intrinsic magnetic moment inside the nucleus. This determination is independent of the coupling scheme operative within the nucleus and of configuration mixing and so on. The difficulty here is the detailed assumptions that we have to make and on which it is very difficult to make a check. Ir is particularly doubtful whether the final state interactions will be sufficiently weak to enable the outgoing nucleon to carry away memory of its initial polarization without significant modification. However, systematic studies involving many nuclei may possibly enable the various disturbing effects to be unravelled.

.4eta Physica Academiae Scientiarum Hungaricae 21, 1966

272 D. H. WlLKINSON

Prospect ing

We know very little about nuclear disintegrations provoked by pions. There m a y be unsuspected and revealing systematic phenomena to be found. I t is worth looking to see.

The use of strange particles

H y p e r n u c l e i

When K- -mesons are absorbed by nuclei the initial act of absorption, which m a y be for example: K - + N --+ A ~ ~- ~r, is often followed by a fur ther process of A~ to forro a hypernucleus in which the A~ subst i tutes for a neutron. An example of such a reaction is: K - A- He 4 -~ - , I-Ie~ A- ~ - . The absorption of Z-hyperons m a y similarly produce hypernuclei following the basic interact ion: Z + N ~ A ~ N. Hypernuclei ate objects of intense interest in their own right; their s tudy falls outside the scope of this present examinat ion al though we m a y note in passing tha t ir m a y bring us information about the wavefunctions of ordinary nuclei, the cores to which the A~ are bound, as well as information about hypernuclei .

A possibly-important use of hypernuclei m a y be to s tudy the stabil i ty of systems tha t are jus t unstable in the free state. The addit ion of a A~ may, by its binding to nucleons, stabilize an unstable nucleon system; our unders tanding of the A ~ N , A ~ N N force m a y then cnable us to make de- ductions about the properties of the unbound nucleon core of the particle- stable hypernucleus. For example, the unstable nucleon systems n 3, n 4, H 4, I-I 5, He 7 m a y serve as the cores of the possibly-particle-stable hypernuclei n~, n~, H~, H i , He s. These hypernuclei could be identif iably formed in, for example, the following reactions:

2Y- -[- He4 --~ n�93 -+-p,

K - + He~-+ n~ + ~ r + ,

2~- + Li 6 --~ n~ -~ 2p ,

K - A- Li6--~ n~ + zt+ - I -P,

K - + Li 6-+ H~ A- p ,

K - -4- LiT---~ H~ -~-P,

K - -4- Li s--~ H~ A- ~r+ ,

K - ~- LiT--+ I-I~ -~-p,

K - -~- Be 9 ~ He s -f- p .

Acto Physiea Academiae Scientiarum Hungaricae 21, 1966


Another i m p o r t a n t p roper ty of hypernucle i is t h a t they can, in thei r decay, popula te high isotopic spin states t h a t are difficult of access by other means. For example, the decay He~-+ Li 4. -t- ~r- can popula te T = 2 states of Li a which may show up as sharp states revealed by a monokinet ic zr--group [12]. Such states m a y be sharp because thei r decay is inhibi ted ei ther b y isotopic spin or by k inemat ic factors.

I t is possible t h a t a s tudy of exci ted states of hypernucle i m a y bring us informat ion about radia t ive t ransi t ion probabili t ies of the hypernucleus cores t h a t ir is ve ry difficult to obtain by o ther means. Consider, for example, the f i rs t exci ted J~ = 2 + s ta te of He 6 at 1,71 MeV. I t is ve ry im p o r t an t to determine the l ifet ime of this s tate for its electric quadrupole t rans i t ion to the ground s ta te of He G since, according to the simple shell model configurat ion, (ls1/~) 4 ( lp) 2, the radia t ion is due to two neut rons only and so the lifetime should be ex t remely long (infinite ir one uses harmonic oscillator wavefunct ions which must be quite a good approx imat ion to the t r u t h here). However , we know from experience in light nuclei t h a t E2 transi t ions take place much more readily t han the simple shell model suggests and, b y analogy with the notorious case in 017, we might guess t ha t this E2 l ifet ime now under con- sideration will not be as long as we should predict f rom the simple model. Since this He 6 sys tem is so ex t remely simple we have a good chance of carrying out the kind of expliei t conf igurat ion- interact ion calculat ion tha t is necessary ir we are to unders tand the detailed mechanism of these E2 enhancements . Unfor tuna te ly , the s ta te in quest ion is unstable against d is integrat ion He 6 -+ -+ He 4 + 2n and so there is no chance of measuring the l ifet ime direct ly. However , when a A ~ hyperon is a t t ached to He 6 ir forms the part icle-stable hypernucleus HeZ, the first exci ted s ta te of which is p robab ly also particle- stable and m a y be though t of as the f irs t exci ted s ta te of He ~ to whieh a r176 has been a t tached. If, as is likely, this exci ted I-Ie 7 s tate has J-~ = 5/2 + its radia t ive de-exci ta t ion to the J~ = 1/2 + ground s ta te will be closely related to the E2 t ransi t ion in He 6 t ha t we are diseussing. Ah interest ing and amusing aspect of the si tuation is t h a t He 7 contains its own buih- in clock in the form of the decay of the A~ A ~ -+ N -t- zt which will be compet i t ive wi th the radia t ive de-exci tat ion. A measurement of the branching rat io of the exci ted He 7 s ta te as be tween gamma-emission and hyperon decay therefore gives us a measure of the l ifetime for the radia t ive process. We must , of course, be able to take into account the effect on the hyperon decay l ifet ime of its binding into the hypernucleus bu t this can be ra the r accura te ly es t imated f rom lifetime studies on hypernuc lear ground states.

The texture of the nuclear surface

We have a l ready discussed one aspect of the capture of s topped K - - mesons by complex nuclei. We explained t h a t the capture m a y well be peri-

,4cta Physica Academiae ScienSiarum H,mgaricae 21, 1966

27/[. D . H . W1LKIN5ON

pheral, in the nuclear s t ra tosphere , and t ha t this capture can therefore br ing us informat ion about the s ta te of the nucleus in its tenuous outer reaehes. An expe¡ aspect of this capture is tha t ir occurs v e ry f requent ly (about 20% of the time) not mesonically on single nucleons th rough reactions such as K - q- N -+ A or S + ~r bu t b y non-mesonic absorpt ion on corre la ted nucleon pairs by the reactions: K - + NN--~ A or I A- N. T h e probabi l i ty of such non-mesonic capture is ve ry closely the same in complex nuclei as it is in He 4. I f the capture is indeed per ipheral this can only mean tha t in the tenuous outer reaches of the nucleus nucleons ate as closely correlated as t he y ate in the alpha-part icle. The nuclear s t ra tosphere is therefore not composed of a more-and-more- tenuous gas of single nucleons get t ing fur ther and fur ther apar t bu t r a the r of sub-nuclear entities t h a t we might t en ta t ive ly label "alpha-particles'; these ate p resumably cons tan t ly dissolving and falling back into the body of the nucleus and reforming elsewhere in the s t ra tosphere [13]. I f this is t rue it is obviously nuclear s t ructure in format ion of the ve ry first impor tance : the surface of the nucleus is not "smooth" bu t "knobbly".

I t mus t be said at once tha t there is some evidence tha t K - - m e s o n capture at rest is not in fac t peripheral bu t takes place in the body of the nucleus in which case the present considerat ions ate not re levant . W h e th e r or not the capture is peripheral may be de termined by s tudying the K-mesonic X-rays in jus t the same way as the muonic and pionic X-rays have been s tudied as a l ready discussed: if the K-mesonic X-rays seen correspond to t ransi t ions between circular orbits and t e rmina te as expected for per ipheral capture then the case is proved, h is wor th not ing t h a t ir the normal capture process is found to be not overwhelmingly per ipheral then we can still select ou t cases of surface capture b y gating our de tec tor for the absorpt ion produc ts on the appropr ia te K-mesonic X-ray , i.e. one corresponding to a t ransi t ion to a circular orbit f rom which capture is overwhelmingly more probable than a fu r the r radia t ive transi t ion. In this way it will be possible to f i he r f rom the bulk of the absorpt ion process jus t those t h a t are peripheral; this complicates the exper iments bu t adds no d i f f icuhy of principle.

High momentum states

I t is possible to look for high m o m e n t u m states in strange part iele absorpt ion processes, for example the react ion: C a2 ~- K - -+ C 11 -4- 2;- in which the C 11 is left in tac t in an identif ied s ta te signals high m o m e n t u m in the absorbing neutron. Similarly the react ion: C 12 -4- Z'- --, B 12 q- A ~ m a y be used for looking f o r a high m o m e n t u m proton. These two types of reac t ion are complemen ta ry in t ha t t hey are sensitive to different high m o m e n t u m states.


A FEW USES OF ELEMENTARY PARTICLES 275

Three-body forces

A section of nuclear s t ructure physics about which we are qui te astonish- ingly ignorant is the impor tance of th ree -body forces. We a t t e m p t to discuss the propert ies of complex nuclei as though only two-body forces opera ted between nucleons. We know ve ry well t ha t th ree -body forces mus t exist bu t have effectively no idea at all at the m o m e n t about their impor tance relat ive to two-body forces .The closest studies of the th ree-body systems, H 3 and He '~ are not ye t good enough to approach this problem. I f th ree -body forces exist they will t end to f avour t r iangular nucleon configurat ions in which the momentum is shared more or less equally among the three nucleons. I f we consider for example the react ion: He 3 -~- K - ~ 27- + 2p using s topped K - - m e s o n s then if two-body forces ate dominant we shall expect to f ind final states consisting of a 27-p pair in a high m o m c n t u m state with the fu r the r pro ton a s a low-momentum spectator . I f th ree -body forces ate impor t an t t h ey will show up in events in which all three particles in the final state have high momentum. The analysis will be complicated as usual by the possibili ty of initial two- nucleon absorpt ion followed by high m o m e n t u m being t ransferred to the originally specta tor part icle by a final s ta te collision with one of the original pair. However , in so simple a system as He z, we have a chance to sort this out and still to p inpoint the th ree-body forces if they are at all reasonably strong. (We m a y note t ha t pion absorpt ion is also a possible way of looking for these correlations bu t K - - m e s o n absorpt ion will be easier to analyze since all final- s ta te particles are then charged. The react ion: ~+ + He 3 --+ 3p also produces all charged particles in the final s ta te bu t is not so sa t is factory because the incident pion must now bring in significant m o m e n t u m and so increases the probabi l i ty of a more-or-less-equal sharing of the m o m e n t u m in the final s tate among the three p roduc t particles.)

Conclusion

This has only been a light and selective passage over somc of the ways in which e lementa ry particles may be used as nuclear probes. Significant informat ion may be had in other ways, for example by the use of ant iprotons and, when sufficient f luxes are available, of neutrinos. There is no doubt tha t here is a field of considerable richness whose exploi ta t ion only awaits the making available of adequate resources.

5 Ae~a Physica Academiae Scientiarum Hungaricae 21, 1966

276 I). H. W1LKII~SON

REFERENCES

1. E. D. COURANT, Phys. Rey., 94, 1081, 1954. 2. A. ABAS]tIAN, R. COOL and J. W. CROI~JN, Phys. Rey., 104, 855, 1956. 3. R. A. SCm~ACK, Phys. Rey., 140, B897, 1965. 4. P. B. JoNEs, Phil. Mag., 3, 33, 1958. 5. Los Alamos Scientific Laboratory Proposal for a High-Flux Meson Factory September

1964 (unpublished). 6. L. N. Coovzi~ and E. M. HENLEY, Phys. Rev., 92, 801, 1953.

H. L. Ar~DERSOI% C. S. JOHNSON and E. P. HINKS, Phys. Rcv., 130, 2468, 1963. 7. S. DEVONS, Proceedings of the Rutherford Jubilee International Conference 1961,Heywood,

p. 611. 8. M. ERJCSOI~ and T. E. O. ERICSON, Ann. Phys. (in course of publieation). 9. S. OZAKI, H. WEINSTEIN, G. GL~.SS, E. LOH, L. NEIMALA and A. WATTENBERG, Phys.

i~ev. Letters, 4, 533, 1960. 10. D. S. KOLTUN and A. REITXN, Phys. Rey., 139, B1372, 1965. 11. G. RAMACHAI~DRAN and V. DEVXNATnAI% Nuclear Physics, 50, 593, 1964. 12. M. J. BENISTON, B. KItISHNAMURTHY, R. LEVI SETTI and M. RAYMU1ND, Phys. Rey.

Letters, 13, 553, 1964. 13. D. H. WILKINSON, Phil. Mag., 4, 215, 1959.

O HEIZOTOPblX HCI-IOJ-lb3OBAHH~IX 3JIEMEHTAPHblX qACTHLI B H3YqEHHH CTPYI~TYPbl ~I~EP

,II~. F. YHJ'IKHHCOH

Pe3~oMe

~aeTc~ clIeRHaJIbHt,I~… o6aop HeCKOJIbKHX npHeMOB, B paMKax KoT0pbIx {~3J~eMeHTap- HbIe qacTHILbl}~ H MeT0~bl ~H3HKH BhlC0KHX 3HepFH~I MOFyT HCII0Ylb30BaTbCR ~YI~I HCCJIe~0BaHH~I ~I~epH0~ cTpyKTypbl. I]o~IqepKHBaeTc~I, qT0 sarna CH0C06HOCTb IIoJIyqHTb HOByt0 HH~0pMaRVIIO 0 CTpyKType a~pa Ha HeKOTOpblx 3KCl]epHMeHTOB qacTo 0FpaHHqHBaeTc~ HaIIIHM He3HaHHeM Ha ~IaHHOM 3Tane ~pyrnx CT0p0H ~~epnofi cTpyKTypM.

Acta Physica Ar Sr Hungaricae 21, 1966

Documents

A few uses of elementary particles in nuclear structure studies