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Hyperf'meInteractions 33(1987)9-17 9 NEW ASPECTS OF THE ATOMIC NUCLEUS D.H. WILKINSON Sussex House, University of Sussex, Falmer, Brighton BN1 9RH, UK Solly Cohen was my oMest and dearest friend. For more than forty years we laughed and /oked - even about physics. He had a great capacity for sceptical wonderment; this quality is needed to read this short tribute to him and to his love for science. 1. Introduction The atomic nucleus is now quite old: well over seventy. Is it showing signs of going into retirement? I can not see that it is, from any point of view. Even those whose passion is for no more than a precise determination of its mass are more active than ever as new regions of the Z, N chart open up under the impact of new projectiles, new targets, new accelerators and new techniques of particle detection and data analysis. And from their accurate mapping of the increasingly steep walls of the stability valley, we are learning about the response of the nucleus to the increasing stress of the Coulomb force on the one side of the valley and to the increasing loneliness of the neutrons on the other. The new probes can also bring in more angular momentum than of yore and we are beginning to learn how the nucleus attempts to protect itself against being spun to destruction. We have begun to gain some under- standing of the nuclear bulk modulus, elusive for so long, that is important not only for the structure of ordinary nuclei but also for that of those giant nuclei of Z --- 1056 ; N ----- 1057 known as neutron stars. We are at last just beginning to identify convincing evidence for what we have long believed, namely that the nucleus is more than the sum of its neutron-proton parts taken pairwise because, for example, a cluster of three nucleons interacts dif- ferently from the sum of the interactions of its three pairs; there is an important collectivism in the life of a nucleus even before we ask what its nucleons are doing. But we also now have dramatic evidence for something else that we have known for a long time, but that has until recently largely escaped our convincing demonstration, J.C. Baltzer A.G., Scientific Publishing Company

New aspects of the atomic nucleus

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Hyperf'me Interactions 33(1987)9-17 9

NEW ASPECTS O F T H E A T O M I C N U C L E U S

D.H. WILKINSON

Sussex House, University o f Sussex, Falmer, Brighton BN1 9RH, UK

Solly Cohen was my oMest and dearest friend. For more than forty years we laughed and /oked - even about physics. He had a great capacity for sceptical wonderment; this quality is needed to read this short tribute to him and to his love for science.

1. Introduction

The atomic nucleus is now quite old: well over seventy. Is it showing signs of going into retirement? I can not see that it is, from any point of view. Even those whose passion is for no more than a precise determination of its mass are more active than ever as new regions of the Z, N chart open up under the impact of new projectiles, new targets, new accelerators and new techniques of particle detection and data analysis. And from their accurate mapping of the increasingly steep walls of the stability valley, we are learning about the response of the nucleus to the increasing stress of the Coulomb force on the one side of the valley and to the increasing loneliness of the neutrons on the other. The new probes can also bring in more angular momentum than of yore and we are beginning to learn how the nucleus attempts to protect itself against being spun to destruction. We have begun to gain some under- standing of the nuclear bulk modulus, elusive for so long, that is important not only for the structure of ordinary nuclei but also for that of those giant nuclei of Z --- 1056 ; N ----- 1057 known as neutron stars.

We are at last just beginning to identify convincing evidence for what we have long believed, namely that the nucleus is more than the sum of its neutron-proton parts taken pairwise because, for example, a cluster of three nucleons interacts dif- ferently from the sum of the interactions of its three pairs; there is an important collectivism in the life of a nucleus even before we ask what its nucleons are doing. But we also now have dramatic evidence for something else that we have known for a long time, but that has until recently largely escaped our convincing demonstration,

�9 J.C. Baltzer A.G., Scientific Publishing Company

10 D.H. l~ilkinson, New aspects o f the atomic nucleus

namely that we can not give an adequate account of even the tranquil low-lying states of nuclei without taking explicitly into account in their own right, not just through their involvement in the generation of the nucleon-nucleon forces, the mesons that are exchanged between nucleons as the agents, or one of the agents, for the propaga- tion of the nuclear force. And we similarly know that we must also take explicitly into account the isobaric excited nucleonic states that the nucleon-nucleon inter- actions inevitably engender by mesonic exchanges and by other means, and also the role of nucleon/anti-nucleon pairs and other relativistic phenomena.

In the foregoing sentences, I have cautiously qualified what until recently could have been regarded as the unique prerogative of mesons in engendering the nuclear force and bringing about isobaric excitations. This, of course, reflects another revolution, now fully upon us, in our thinking not primarily about nuclear structure, but rather about nucleon structure, namely the quark/gluon or QCD revolution. Neutrons and protons are no longer the elementary particles of a few years ago, communicating with each other, without change of form, by discreet exchange of mesonic messages; they are now themselves complex structures of quarks and gluons with an inner region of perfect chirality, the vacuum in the Wigner mode, matching into an outer region as the mesonic field develops, the vacuum there in the Goldstone mode, with hanging overall the unresolved topological question mark of the skyrmion, the non-fluctuating mesonic field that, mysteriously, carries baryon number so that, after complex negotiations, an isolated nucleon fractionates its overall baryon number of unity between its core of quarks and its outer skyrmion/meson mantle.

With such a picture for a nucleons about 1 fm in its radial extent before the structure has died away, we can not hope that this old vision of elementary nucleons interacting solely through mesonic exchange, with or without concomitant excitations into elementary isobars, will have any literal validity, at least until the (complex) nucleons are so far apart that their structures are effectively separated, say at centre- to-centre distances of 1 + 1 = 2 fm or more, when we might hope that we may again talk in the language of mesonic exchanges (the pion only, of course, at such great distances), with the associated force calculable from the empirical properties of the free space pion-nucleon interaction. This indeed turns out to be the case; for example, the higher (g-wave) phase shifts of the NN interaction are quite well described by pion exchange with inferred effective NN separations of greater than 2 fm, but for smaller NN separations (and remember that in a nucleus the average nearest-neighbour NN separation is less than 2 fm) the complex nucleonic structures must overlap more and more significantly and the NN force must increasingly be dominated by the effects of that overlapping of the nucleonic structures and the resulting quark/gluon interchange between those structures. The NN force, although it is no longer proper to speak of it as such since the entity in question is effectively a single multi-quark/ gluon object, is then to be thought of as a sharing of the very substance of the original two nucleons, the re-sorting of them out into two colourless objects taking place as they eventually separate but without any assurance that each contains "the same quarks" that they comprised before they met.

D.H. Wilkinson, New aspects of the atomic nucleus 11

When we compare the 1 fm radial dimension of each nucleon with the "NN centre-to-centre separation" of about 1 fm that is responsible for the greater part of the nuclear binding energy and the few tenths of 1 fm of the "hard core" that plays a crucial role in many aspects of nuclear matter theory and nuclear structure, we see that persistence of this nucleon/meson language for a most important range of nuclear questions can not have the status of much more than a useful parameterization, although I should say that its utility will probably persist to some degree, not least in relating features of the interaction to the quantum numbers involved.

You can, of course, pick up this last point and ask whether all this uncertainty and complication as to nucleon structure and the nature and origin of the NN force at short distances really matters for our description and understanding of complex nuclei. Is it not enough to base ourselves on the empirically-determined free space NN inter- action and to convert this through bubble diagrams and the like into an effective NN interaction within the nuclear medium? Or, recognizing the great difficulty of making this latter step in any definitive and unambiguous way (even leaving out of account the evident importance of true many-body forces), rather use simple empirical two-body matrix elements such as has been spectacularly successful in the lp shell and in the 2s, ld shell?

In any case, you may argue further, at almost every rum we have to augment an understanding based on a microscopic description of the nucleus by the additional effects of collective oscillations and vibrations of the nucleus as a whole, with or without neutron/proton discrimination, so that the underlying structure of the nucleon itself is wholly obscured and therefore a matter of no importance for complex nuclei. If quarks and gluons are of explicit importance for the structure of the complex nucleus where, you ask, is the smoking gun? That is a good question that certainly can not yet be answered, but before dismissing it too firmly, it is salutary to bear in mind that the smoking gun of mesonic contributions to nuclear effects has only been evidenced comparatively recently, and that Nature may be more self-revelatory in respect of quark effects than we now see. It is a matter of taste and for the moment best left at that. It is clearly of the greatest interest and importance to study nucleon structure and to attempt, through that, to understand the fundamental origins and mechanisms of the NN interaction at all distances, bearing modestly in mind as we do so that even for large NN separations, where we successfully give an account in terms of empirical lrNN properties as already remarked, we do not yet fully understand the essential pion itself, whether it is quark-based or whether it enjoys an elementarity of its own as the Goldstone boson of chiral symmetry breaking, or whether the latter can be seen as a collectivity among q~ excitations, or whether it is a piece of painfully negotiated machinery incorporating all these things in differing measure. But there is certainly little pressure at the moment to introduce explicit quarks into our dis- cussions of the low4ying level structure of i so Hf.

12 D.H. Wilkinson, New aspects o f the atomic nucleus

However, if we look at a nucleus by the same methods that have brought us information about nucleon structure, that is to say by the deep inelastic scattering of electrons and muons, we can at least say whether the overall momentum distribu- tion of the quarks in the nucleus is the same as in the nucleon. As is well known - the EMC effect - it is not: in a complex nucleus there is a clear deficiency of quarks in the intermediate momentum range relative to those in a free nucleon and, not so clearly, an excess in the low momentum range. (All this after appropriate - not unambiguous - allowance for the effect of the Fermi motion of the nucleons in the nucleus.) A nuclear physicist knows that when you bind nucleons together to con- struct a nucleus that binding comes about only because the proximity of one nucleon to another emboldens the atmospheric mesons, normally emitted by the one nucleon and reabsorbed by it itself, rather to venture into the space between the nucleons

and be absorbed by the other nucleon. The nuclear physicist therefore expects deep inelastic scattering on a nucleus to take place not only from the quarks of the original nucleons, whether central or constituent to the atmospheric mesons, which original nucleons he imagines to be unchanged by the binding, but also from the quarks of the mesons that the scattering process catches "in the air" on their way from one nucleon to another to bring about the NN binding. The quark momentum distribution of these mesons in transit must therefore be added to that of the nucleons themselves, thereby modifying the overall quark momentum distribution as observed.

The nuclear physicist also recognizes that some nucleons in the nucleus are not in their ground states but in excited isobaric states, where the quark momentum distribution will be different from that of the ground states.

Indeed, when these effects are estimated it seems not unreasonable that the EMC effect may be due to them. But the particle physicist naturally looks at the process primarily from the point of view of the nucleons themselves, since he is not interested in the ways in which nucleons stick together to make nuclei. The particle physicist therefore sees the modification of the overall quark momentum distribution in the EMC effect as a signal that immersion of nucleons in the nuclear medium changes the quark momentum distribution within the individual nucleons. Indeed, by examining the departure from scaling exhibited by isolated nucleons, one can see that the EMC effect can be well represented by the remark that nucleons bound into a nucleus respond to the virtual photon probe as though the probing momentum transfer were itself simply scaled to a consistently lower fraction of that appropriate for a free nucleon. This parameterizes away the effect but does not reveal the seat of the physics. A more mechanistic approach is to ask how we might expect the structure of a nucleon to be modified when we immerse it in the nuclear medium, thereby exposing the quarks of the one nucleon to the overall field associated with the quarks of neighbouring nucleons. As may be imagined, in our present degree of ignorance as to the details of nucleon structure, this question can not be answered uniquely but some model calculations have shown that it might not be unreasonable that the effect

D.H. Willa'nson, New aspects o f the atomic nucleus 13

of this immersion should be to produce the 50% swelling of the nucleon (by volume) necessary to produce the observed EMC effect, interpreted as a rescaling phenomenon in terms of the probing momentum transfer. It should, however, both be said that other model calculations produce a nucleon shrinkage rather than a swelling, and that the necessary 50% swelling would very probably produce such other changes in intrinsic properties, for example magnetic moments and the energy of the 33-isobar, as would be very difficult to assimilate.

As we learn more about the nucleus, we also learn how much more there is to know: our increasing ignorance outstrips our increasing knowledge. We also realize how superficial is our knowledge of the nucleus, both in the sense that our quantita- tive experiments barely scratch the nuclear periphery and in the sense that our quanti- tative theories barely dip below the Fermi surface. To be sure, we can blow the nucleus apart and look at its fragments, and from such studies we shall surely eventually learn much of tremendous importance about nuclear matter under extreme conditions of compression and rarefaction, about the liquid/gas phase transition, about condensation phenomena and the quark-gluon plasma, but as yet this work is inchoate and barely propaedeutical. A very few precious experiments relate to specific microscopic aspects of the deep interior of the nucleus and we are also gaining much important informa- tion, from inelastic electron scattering, about the volume distribution of transition moments, but these are global properties in respect to an underlying microscopic understanding and are not in themselves specific and prescriptive in their relationship to the behaviour, in the nuclear interior, of individual nucleons, mesonic currents and SO o n .

The object of this lengthy introduction has been to skim lightly over a few of the fundamental uncertainties that stand between us and what we might term a top-down understanding of ordinary every-day atomic nuclei: from QCD to 18~ A supplementary objective has been to prepare the reader's mind for the notion that while we are so far from anything like a complete understanding of ordinary nuclei, we must not ignore the possibility that there may exist extra-ordinary nuclei that differ from those of our usual experience in radical ways. Ordinary nuclei are basically made out of neutrons and protons, they are more-or-less spherical (a nucleus as non- spherical as an American football is regarded as a rather extreme excursion) and they are of more-or-less uniform and constant density. But may there not exist nuclei, equally made out of neutrons and protons, that are of a form remote from a more- or-less sphere? And may there not exist nuclei, in the sense of long-lived objects held together by strong forces of which we already have experience, that are not just made out of neutrons and protons but have as essential and permanent, not virtual and transitory, constituents other of the great menagerie of particles of which we are now aware? The rest of this paper exposes, in a little detail, just one of many possibilities in each of these radical and exotic categories. It should be immediately emphasized that although the possibilities to be presented are speculative,

14 D.H. Wilkinson, New aspects o f the atomic nucleus

they are speculative within hard and well-established principles, so that the chief question is not whether or not the objects to be discussed can exist, but rather whether they can be put into evidence; their abundance in the circumstances of the world as we have it or as we can bring it to be.

2. S t range m a t t e r

Ordinary nuclei are made out of neutrons and protons, but neutrons and protons are themselves made out of two species of quarks, u and d, which are very light, possibly massless. Neutrons and protons are quite close together in the nucleus and often interact at distances comparable with, or less than, their own dimensions. Why do the quarks not spill out of the nucl.eons and simply fill the nucleus as a u, d quark gas? We do not know that they do not do this to some degree: at least we do not know that a move towards this is not made by there being a certain n u m b e r o f 6q, 9 q . . . (transitory) entities in the nucleus at any moment and one strongly suspects that there are. But we do know that for the most part the quarks in the nucleus remain clustered into nucleons, probably with frequent quark/gluon exchange between nucleons, as already discussed, and probably with occasional larger 6q, 9 q . . . fusions, as just remarked. We can not claim fully to understand this in our present state of uncertainty about nucleon structure, but that it is a fact must be an important con- straint on our modelling of the nucleon. For some reason, the energy of the (A + Z ) u + (A + N)d Fermi gas is greate.r than that of the Zp + Nn Fermi gas.

But now suppose we introduce strange (s) quarks into the system. Since the mass of s is greater than that of u and d (the mass of strange baryons is greater than that of their ordinary counterparts), we should expect the mass of such a composite system to be greater than that of an ordinary system containing the same total number of quarks. However, consider what happens if all the quarks spill out into a single u, d, s Fermi gas. The Fermi energy of such a gas of three distinguishable fermions is less than that of the same number of only two types by the factor, for equal numbers of (massless) quarks of all types, [3/(1 + 24/3)] a/4 = 0.89 [1]. There is therefore an energy gain in such spilling out that has to be set against the greater mass of the s quark and against the confinement mysteries that lead to a preference for n, p nuclei over u, d nuclei. However, calculations via MIT bag and Fermi gas models as functions of the s-quark mass, the QCD fine structure constant and the bag pressure constant show that for reasonable values of these parameters, such u, d, s Fermi gases might be energetically absolutely stable for systems ranging from the A-values of ordinary nuclei up to the indefinitely high masses of the black hole.

We are thus faced with the fascinating possibility of the existence of sorts of objects new to our experience, of density comparable with that of ordinary nuclear matter (as the calculations suggest) but of possibly large mass, up to that of stars or beyond. Of course, the possibilities for the creation of such objects today is distinctly

D.H. Wilkinson, New aspects o f the atomic nucleus 15

limited, but it is by no means implausible that they might have been formed, possibly in great abundance, in the phase transition that followed the free-quark plasma of the earliest moments after the Big Bang. In that case, they should still be around; they have, indeed, been suggested as a candidate for the notorious missing mass of today's observable universe. Abundance limits exist, but only for certain mass ranges, and further searches would be of great interest.

An obvious question, and possibly even a point of some anxiety, is why, if this strange matter represents the true nuclear ground state, do ordinary nuclei, such as those out of which we are ourselves composed, not spontaneously transform into this other state? So they could, and possibly do. The point is, however, that to gain from the lower Fermi energy of the u, d, s quark gas a large number of u, d quarks would have to transform simultaneously into s quarks (we know that the familiar hypernuclei are heavier than their corresponding ordinary nuclei), and this would be a weak interaction of such high order that its transition rate is negligible even on cosmological, let alone human, time scales. Breathe freely.

3. Nuclear rings and chains

We have just looked at a truly radical new form of nuclear matter that we may search for with sceptical wonderment but that we can not otherwise do much about because the conditions for its possible formation are no longer available. The other classes of novel nuclear object to which reference was made at the end of the intro- duction are forms of organization of ordinary nuclear stuff, namely neutrons and protons, into shapes and conditions remote from the more-or-less spherical nuclei of our ordinary experience. It has been suggested [2] that under conditions of stellar collapse, nuclear matter may display preferred forms resembling Swiss cheese, lasagna or spaghetti and that in certain respects, heavy ion collisions may duplicate such gastronomical conditions. The very different possibility now to be presented also starts from consideration of heavy ion collisions.

Energetic conditions between heavy ions can involve large amounts of angular momentum. To illustrate this, consider identical colliding nuclei of mass A. Collisions with a finite impact parameter contain angular momentum Jf units in the region of geometrical nuclear overlap, containing A f (~< 2A) nucleons, between the two nuclei. Figure 1 shows Jf as a function of Af for A = 50, 100 and 200 for a (laboratory) bombarding energy of 2 GeV/nucleon, such as is presently available. We see that very large values of Jf result.

Although we can not expect that the collision will actually result in a nucleonic system of mass Af rotating with Jr, it is likely that such collisions will not infrequently have as partial residue, deriving from an initially expanded low-density nucleonic blob, systems with nucleon number a not insignificant fraction of Af rotating with a not insignificant fraction of Jr. As this residual system evolves, it will flatten and light

16 D.H. Wilkinson, New aspects of the atomic nucleus

I I I I

1500

1000

A-200

500

A =100

01.. 0

A=50

100 200 300 t~00

Af

Fig. 1. Identical nuclei of A-value as indicated on the curves collide at 2 GeV/nucleon for the bombarding particle. Their geometrical overlap con- tains Af nucleons; the angular momentum residing in this overlap is Jf units.

nuclei will condense out within it. By far the most likely initial product of such recombinant nucleosynthesis is alpha particles on account of their uniquely tight binding and high density (twice that of lead at their centre) and resistance to further nucleosynthesis owing to the instability of the A = 5 systems. (Note also that the light nuclei beyond helium, certainly up to and including the boron isotopes, factor rather realistically into alpha particles plus additional nucleons so that their possible formation in this phase of our consideration would not vitiate our focus upon alpha particles as the dominant nuclear constituent of the recombinant system.) The alpha particles will move centrifugally towards the edge of the spinning flattened disc, there forming a ring in an atmosphere of, chiefly, excess neutrons.

This naturally leads us to ask whether a spinning ring of alpha particles plus some circumambient neutrons is stable against dissociation into its constituents. The answer seems to be yes, and detailed investigation shows that it is likely that the

D.H. Wilkinson, New aspects of the atomic nucleus 17

previous phases of condensation, alpha-particle formation and flattening can also be safely negotiated [3]. Such alpha-neutron rings appear to be stable at least up to J - 60 for 10 alpha particles and up to J -~ 200 for 20 alpha particles (assuming 2 neutrons per alpha particle, which is reasonable). As we see from fig. 1, such angular momenta, which effectively stabilize the rings against collapse into conventional nuclei, should be readily available.

Although these alpha-neutron rings are stable against dissociation into their (alpha particle plus neutron) constituents up to high values of angular momentum, they are usually unstable against breaking open into long alpha-neutron chains, but this takes time, typically 10 -1~ sec, because of the effective Coulomb barrier faced following the breaking of the alpha-alpha nuclear bond, so that observation of the properties of the rings may be possible. The chains into which the rings open are also stable against dissociation into their constituent alpha particles and neutrons up to angular momenta at least as great as those that can be held by the rings. Their lifetime against further breakup into shorter chains, which is sometimes possible, is also typically of the order of 10-1 o sec; their lifetimes against electromagnetic de-excitation to a J-value no longer able centrifugally to stabilize them against collapse into con- ventional nuclei is about 10 -9 sec, SO for the chains as for the rings, experimental observation may be possible.

The rings have diameters of about Na fm, where Na is the number of alpha particles that they contain; the chains have lengths of about 3Na fm, so that the nucleus 120 Zr in this condition has the formidable dimension of 60 fm.

This is probably a good point of sceptical wonderment at which to break off this story and to recall the expression that came over SoUy's face when he did not want you to know whether or not he thought you wanted him to think you were being serious or not.

References

[1] A. De Rujula, Nucl. Phys. A434(1985)605c; see this paper for references to all matters of this section.

[2] C.J. Pethick, Nucl. Phys. A434(1985)587c, q.v. for relevant references. [3] D.H. Wilkinson, Nucl. Phys. A452(1986)296.