17
Nuclear Physics A180 (I 972) 385-401; @ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher NUCLEAR SPECTROSCOPY WITH HEAVY-ION INDUCED PROTON-TRANSFER REACTIONS IN LIGHT NUCLEI URSULA C. SCHLOTTHAUER-VOOS, H. G. BOHLEN, W. VON OERTZEN and R. BOCK t Physikalisches Institut der Universitiit, Marburg, Germany and Max Planck Institut ftir Kernphysik, Heidelberg, Germany Received 13 August 1971 Abstract: Angular distributions of the proton-transfer reactions llB(lsO, “N)‘*C at &, = 27. 30, 32.5,35 and 60 MeV and 1zC(19F, 2aNe)1’B at ,I& = 40.60 and 68.8 MeV to ground and excited states of both final nuclei were measured. A DWBA analysis based on the method of Buttle and Gohifarb shows, that a consistent description of all data is possible with those optical- model parameters, which are obtained from the analysis of the elastic scattering data by applying the concept of strong absorption. The relative spectroscopic factors are independent of energy and in good agreement with theoretical values and those obtained by conventional reactions. The absolute values agree within a factor 1.5 in the 160 on I’B case. ELASTIC SCATTERING llB(lsO, lsO), E = 27, 30, 32.5 and 35 MeV; “C(19F, 19F), E = 40, 60 and 68.8 MeV; measured do/d&‘(B); deduced optical- E model parameters. NUCLEAR REACTIONS “B(‘sO, 15N)‘%, E = 27. 30, 32.5, 35 and 60 MeV; ‘*C(19F, “‘Ne)“B, E = 40, 60 and 68.8 MeV; measured du/d(a@). DWBA analysis. “B, “C. “N, l”Ne deduced spectroscopic factors. 1. rntroductioo The investigation of one-nucleon transfer reactions between heavy ions above the Coulomb barrier has been performed in many cases with the aim to study the reaction mechanism of the heavy-ion reactions, especially with respect to the possible extra- polation to multinucleon transfer reactions l-‘)_ In most cases satisfactory quali- tative interpretations of the measured data were achieved. Only very few attempts of a quantitative analysis exist s-8), due to the theoretical and mathematical problems characteristic to heavy-ion transfer reactions. The zero-range DWBA, convenient and successful for the analysis of stripping and pick-up reactions induced by conventional projectiles, is no longer valid for heavy-ion transfer reactions. Finite-range calculations, on the other hand, require more complicated and extensive methods. + Present address: GSI, Darmstadt, Germany. 385

Nuclear spectroscopy with heavy-ion induced proton-transfer reactions in light nuclei

Embed Size (px)

Citation preview

Nuclear Physics A180 (I 972) 385-401; @ North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

NUCLEAR SPECTROSCOPY

WITH HEAVY-ION INDUCED PROTON-TRANSFER REACTIONS

IN LIGHT NUCLEI

URSULA C. SCHLOTTHAUER-VOOS, H. G. BOHLEN, W. VON OERTZEN and R. BOCK t

Physikalisches Institut der Universitiit, Marburg, Germany and

Max Planck Institut ftir Kernphysik, Heidelberg, Germany

Received 13 August 1971

Abstract: Angular distributions of the proton-transfer reactions llB(lsO, “N)‘*C at &, = 27. 30, 32.5,35 and 60 MeV and 1zC(19F, 2aNe)1’B at ,I& = 40.60 and 68.8 MeV to ground and excited states of both final nuclei were measured. A DWBA analysis based on the method of Buttle and Gohifarb shows, that a consistent description of all data is possible with those optical- model parameters, which are obtained from the analysis of the elastic scattering data by applying the concept of strong absorption. The relative spectroscopic factors are independent of energy and in good agreement with theoretical values and those obtained by conventional reactions. The absolute values agree within a factor 1.5 in the 160 on I’B case.

ELASTIC SCATTERING llB(lsO, lsO), E = 27, 30, 32.5 and 35 MeV; “C(19F, 19F), E = 40, 60 and 68.8 MeV; measured do/d&‘(B); deduced optical-

E model parameters. NUCLEAR REACTIONS “B(‘sO, 15N)‘%, E = 27. 30, 32.5, 35 and 60 MeV; ‘*C(19F, “‘Ne)“B, E = 40, 60 and 68.8 MeV; measured du/d(a@). DWBA

analysis. “B, “C. “N, l”Ne deduced spectroscopic factors.

1. rntroductioo

The investigation of one-nucleon transfer reactions between heavy ions above the Coulomb barrier has been performed in many cases with the aim to study the reaction mechanism of the heavy-ion reactions, especially with respect to the possible extra- polation to multinucleon transfer reactions l-‘)_ In most cases satisfactory quali-

tative interpretations of the measured data were achieved. Only very few attempts of a quantitative analysis exist s-8), due to the theoretical and mathematical problems characteristic to heavy-ion transfer reactions.

The zero-range DWBA, convenient and successful for the analysis of stripping and pick-up reactions induced by conventional projectiles, is no longer valid for heavy-ion transfer reactions. Finite-range calculations, on the other hand, require more complicated and extensive methods.

+ Present address: GSI, Darmstadt, Germany.

385

386 U. C. SCHLOTTHAUER-VOOS et al.

However, as heavy ions are strongly absorbed at small impact parameters in a col- lision the reduction of the six-dimensional integral of the DWBA transition ampli- tude to the three-dimensional integral given by Buttle and Goldfarb “) may be used. This approach, originally derived for subcoulomb transfer reactions, is nevertheless applicable at the higher energies, because the strongly absorbing optical potentials give the necessary localization in configuration space. The DWBA approximation, which may not be valid for the strongly absorbed partial waves ‘), should give good results, if the reaction is determined by the relatively weakly absorbed surface waves, which are well determined by the optical model.

Indeed, it was shown, that with the concept of strong absorption a consistent de- scription of different elastic scattering data over a wide range of energies was possible [ref. lo)]. However, until now, no systematic and satisfactory analysis of heavy-ion induced proton-transfer reactions exists.

It was the aim of this analysis to test, in how far a consistent description of dif- ferent heavy-ion transfer reactions over a wide range of energies is possible. Angular distributions of the proton-transfer reactions 11B(160, “N)“C at 27, 30, 32.5, 35 and 60 MeV incident energy and 12C(rgF, ‘ONe)“B at 40, 60 and 68.8 MeV have been measured to ground states and excited states of both final nuclei. The optical- model parameters for the DWBA calculations were extracted from the analysis of the elastic scattering. It is the intention to show, that with the concept of strong ab- sorption the different reactions could be described with almost the same parameters at various energies and that the extracted spectroscopic factors are independent of energy and in agreement with those obtained by conventional reactions and methods.

2. Experimental technique

The experiments were performed at the Heidelberg EN and MP tandem Van de Graaff accelerators. The reaction products were analysed by the usual AE/E technique, the AE detector being a gas-filled proportional counter, the E detector a silicon sur- face barrier counter. With targets of about 80 pg/cm2 and windows of 1 x 2.5 mm2 in a distance of 250 mm from the target, the total energy resolution was 150-200 keV for light reaction products (Li to C) and about 400 keV for heavy elements as Ne.

The absolute cross sections were obtained by normalizing the elastic-scattering data to the Rutherford scattering measured at lower energies with the same experimental arrangement. Therefore errors arise mainly by the uncertainty of the angle and by possible changes in the charge state of the incident beam [see also ref. ‘“)I. It turned out, that the absolute cross section of the I60 on llB data at 27,30,32.5 and 35 MeV incident energy, given earlier lo, ‘I), had to be raised by a factor of 1.5. The error in the absolute cross section is about + 15 % for the 35 and 68.8 MeV data and about + 25 % for the low-energy data.

PROTON TRANSFER 387

3. Theory

The data were analysed with DWBA calculations by using the method of Buttle and Goldfarb “) for the reduction of the DWBA amplitude to a three-dimensional integral which can be calculated in a conventional DWBA code.

Generally the transition amplitude for the reaction A(a, b)B = A([b+x], b)[A+x] is given by the expression “):

T = drdrbx ~r-‘*(rr)(BblV(r,,)JaA)~I”(ri), s (1)

4i and #Jo are the scattering waves in the entrance and exit channel, for the definition of the radii see fig. 1. The spins of the particles involved are J,,, J,,, j., j,, and S, with z-components IU,, MB, ma, mb and m,. The transferred particle is bound in the en- trance and exit channel with total spin jllr (z-component pilr) and angular momentum Zilr (z-component m,,,) which are connected by the relation ii/f = I,,r +s,.

b

Fig. 1. Definition of the radii used in the DWBA.

By calculating the overlap integrals (bla) and (BIA), eq. (1) can be written:

f$:i and O:fii are the spectroscopic factors for the particle x whose bound state wave .

function 1s given by #’ and $r. The z-components in the Clebsch-Gordan coeffi-

cients are omitted. This six-dimensional integral (2) can be reduced following Buttle and Goldfarb

with the assumptions: (a) the mass of the transferred particle x is small as compared to the mass of

the cores A, b, x << A and x < b, giving:

(b) The asymptotic behaviour of the bound state wave function

$7 only is important.

388 U. C. SCHLO~HAUER-VOOS et al.

Approximation (b), originally used for subcoulomb transfer reactions because of the strong Coulomb interaction, holds if the two nuclei are at large distances; it will still be valid for the higher energies if in recations with complex nuclei strong absorption occurs already at large distances.

Thus for neutron-transfer:

neglecting a phase factor and expressions as (21+ I)*. N2 is the normalization of the asymptotic form as compared to the exact bound state wave function, hi” andjI are spherical Hankel and BesseI functions, Ef is the wave number of the particle x in the final nucleus.

For proton-transfer the asymptotic form of the bound state wave function is de- scribed by a Whittaker function, which, however, may be approximated by a Hankel function “). Therefore the same procedure as above is applicable, only %I is no longer physically determined by the binding energy of the proton, but a parameter to fit the decrease of the Hankel function to the asymptotic behaviour of the bound state wave function.

With these ~sumptions the integral (2) may be separated into two three-dimen- sional integrals:

Nl and Cli correspond to N2 and elf, but belong to the entrance channel. AI, can be calculated by a closed expression:

A,, x (-)I‘ ; Nl cL:‘(cli)-r~- 1,

T;” has the form of a normal zero-range amplitude and may be calculated by conven- tional methods.

In the following analysis the optical-model parameters were extracted from the corresponding data. The normalization constants N,,, and the bilk were found by fitting a Hankel function to the exact bound state wave function g between 5 and about

PROTON TRANSFER 389

18 fm. ‘The former one as lower boundary seems to be a reasonable value, as a cut-off radius up to 5 fm does not influence the DWBA calculation because of the use of strongly absorbing potentials.

The bound state wave function itself was calculated in the usual way by a Woods- Saxon potential with radius parameter r. = 1.25 fm and diffuseness a = 0.65 fm, the depth was determined as to reproduce the binding energy of the proton, the spin- orbit potential was 20 MeV.

The &;” were calculated by the zero-range codes DRC fief, ““)I and JUHE [ref. ‘“)I. No cut-off radius was used in the calculations. The Hankel functions in the integral (6) were repIaced by the correct bound state wave function.

4. Analysis of the data

4.1 e ELASTIC SCATTERING

In order to get optical-model parameters suitable for the DWBA description of the proton-transfer reactions, at first the elastic scattering of the cases involved was ana- lysed. As shown earlier ’ “) th e concept of strong absorption gives a consistent set of parameters, which reproduced nearly a11 measured data simultaneously, With this assumption it was sufFicient to find a description of the real potential in the surface region and to use a deep ~rnag~n~ potential in order to prevent contributions from small internuclear distances to the scattering amplitude. Thus not a single parameter but the potential as a whole may be submitted to physical interpretation.

The angular distributions for the elastic scattering of 19F on “C and of I60 on ‘lB at all measured energies are shown in figs. 2 and 3, together with optical-model pre- dictions. For both, the real and imaginary potentials a Woods-Saxon form factor was chosen:

U(r) = U. (I+exp r?))-‘,

W(r) = I+$ f. +exp ( (Yj)_‘,

where

U(r), p(r) being the rea1 and imaginary potential; r,,, ret the radius parameter of the real and imaginary potential; a,, a, the diffuseness of the real and imaginary poten- tial, and Ar, AP the mass of the target and the projectile.

The calculations were performed with the Fortran program JIB 3 by Perey 14). The parameters, given in table 1, are identical to those, used in previous analysis of other data ’ “> and are the same far a& calculations Only the depth af the imaginary potential was slightly changed accounting for the change in the incident energy. The radius p~ameter of the Coulomb potential was fixed to be 1.45 fm.

390 U. C. SCHLO’M’HAUER-VOOS et a!.

Elastic Scattertng

0” 300 90” 120” SO0 180- @

Figs. 2, 3. Elastic scattering of 160 on ll”B”,nd l*F on 12C with optical-mode1 predictions. The parameters (table 1) are the same for all cases.

The rise at backward angbs in the I60 on “B case is probably due to the competing

five-nucleon transfer Is) “B(160, 11B)160 and has therefore not to be reproduced

by the optical-model calculations. [Some authors made attempts to get a better de- scription of the backward-scattering data using L-dependence of the imaginary poten- tial 16)].

PROTON TRANSFER 391

TABLE 1

Parameters for the optical-model description of the elastic scattering I60 on “B and lQF on 12C (figs. 2 and 3)

rot

(fm)

I60 on llB 60 100 1.19 0.48 30 1.26 0.26 35 27 32.5 25 30 27

l QF on %! 68.8 30 60 27 40 25

4.2. 11B(160, 1sN)‘2C

In the reaction ‘iB(160, r5N)12C (spectrum in fig. 4) only the two proton-hole states of “N are populated as expected, the ground state and the state at 6.32 MeV with spin and parity .J” = +-, 3- and the configuration (p&)-r (F3 160p,S, and (p+)- ’ @ 160g_S. respectively. For 12C transitions to the levels at 4.44 MeV (J” = 2+) and 9.64 MeV (J” = 3-), which are assumed to have large single-panicle widths, are strongly observed.

0 20 40 60 00 100 120 channel

Fig. 4. Energy spectrum of the p-transfer 11B(160, 15N)1zC.

The angular distributions have been measured in the whole range of the c.m. angle. They show a rise with diffraction structure at backward angles according to the com-

392 U. C. SCHLOTTHAUER-VOOS er al.

peting a-transfer reaction r1B(r60, ‘*C)15N, which is connected by eIzc = x--&~ to the proton transfer. As an example the 60 MeV data are shown in fig. 5, the data at the lower energies have already been reported earlier ‘I). Because of the two reac- tions leading to the same exit channel, interference effects are present at angles around 90” c.m. Therefore at 60 MeV only the anguiar distribution up to about 60” c.m. is due to the proton-transfer alone and consequently only this part of the angular dis-

w60, ~~N)I*c

E Lab = 60 MeV

[“jN, “C]

0” 30” 60” 90” 120” 150”

%m

Fig. 5. Experimental angular distributions of the reaction LzB(*60, 1sN)12C at 60 MeV incident energy.

tribution should be described by the DWBA. At lower energies interference effects are important at even smaller angles.

The angular distributions at all measured energies were described by the DWBA discussed above (figs. 6-9). For the transition to the ground and “C states the optical- mode! parameters of the DWBA calculations in entrance and exit channel (table 2) are practically the same as used for the description of the elastic scattering. Only the r. of the real potential was slightly changed from 1.19 fm to 1.17 fm in the entrance

PROTON TRANSFER 393

channel and to 1.16 fm in the exit channel in order to get best fits. parameter set (a)]. Effects on the absolute cross section are negligible.

For the transitions leading to the 4.44 and 9.64 MeV states of “C at 60 MeV the angular distributions calculated with parameter set (a) show too pronounced struc- ture as compared to the experimental data. In order to get better agreement the real diffuseness in the exit channel was changed from 0.48 fm to 0.25 fm [parameter set (b)], for the 9.64 MeV transition even better agreement was found by changing the real diffuseness in the entrance channel in the same way [parameter set (c)l. The same effect could be obtained by changing roi from 1.26 fm to 1.35 fm. The absolute calculated cross section in the maxima remains the same for the different parameters used, so that the spectroscopic factors are not affected by this change in the param- eters.

For the 6.32 MeV transition the optical-model parameters had to be changed more

60 MeV

325 MeV

27 MeV

I I II I I I II I I 0" 30" 60" 90' -o,,,

Fig. 6. See caption Figs. 7 and 8.

394 U. C. SCHLO~HAUER-VOOS et aI.

&**27Me’4 l

10“

~ 0” xp 6o” so’

0 c.m.

Fig. 7.

00 20” 600 Go@ 8 C.l?l.

Fig. 8. Figs. 7 and 8. DWBA calculations for the angular distributions of the p-transfer

11B(160, ~sN)12C. Parameters in table 2.

drastically (table 2), but are the same for all energies. The radius of the real potential in the entrance channel had to be lowered by 10 %.

For calculating the bound state wave functions of the proton the configurations of simple shell-model predictions were taken. For the 2+ and 3- states of “C only

p+ and d+ contributions to the transition amplitude have been considered, in agree-

ment with theoretical calculations t’) and with the procedure in other reactions “* 19).

PROTON TRANSFER 395

Optical-model

l’E(‘sO, ‘5N,,,.)‘2C~.~4

EL*,, = 60 MeV

I

Fig, 9. See caption Figs. I and 8.

TABLET

parameters for the DWBA description of the reaction

7,8,9)

llB(laO, lsN)“zC (figs. 6,

FinaI states (IsN, ‘%)

Initial Final

g.s., g.s.

g.s., 4.44

gs., 9.64

6.63, g.s.

60 100 1.17 0.48 30 1.26 0.26 100 1.16 0.48 30 1.26 0.26

35 21 2-l

32.5 25 25 30 27

60a 30 27 b 0.25

35 27 0.48 25

32.5 25 22 30 27

60a 30 25 b 0.25 C 0.25

60 1.08 0.48 1.06 0.48 27

35 21 25

32.5 25 22 30 27

The bound state wave functions calculated by a Woods-Saxon potential and the cor- responding Hankel functions used in the DWBA calculations are shown in fig. 10. The agreement between s, p waves and Z = 0, I = 1 Hankel functions is excellent

396 U. C. SC~LO~HAUE~-VOOS ef al.

between 5 and 20 fm, even d waves may be approximated by I = 2 Hankel functions

in the range between 5 and 15 fm within limits better t&an 10 %.

The relative spectroscopic factors obtained by this analysis for the transitions

bound state wave functions 9(f)--- and ther approxmatcn by a hankel function

0 3 6 9 12 15 18

r/fm

Fig. 10. Comparison of bound state wave functions calculated by a Woods-Saxon potential and the approximate Hankel function used in the calculations.

TABLE 3

Relative spectroscopic factors 82/8*...2 for the transition “B,.,. +p --j. *%I

Final state in 12C

bound state

This experiment (‘*C, “B) t3He, d) Theory “) .-- ___-__ __ ‘1

EM WeV) .____- -_

27 30 32.5 35 60

gs. (Jr = o+) P+ I 1 1 1 I 1 1 1 4.44 (JR = 2+) p* 0.09 0.16 0.11 0.12 0.12 0.10 0.17 “) 0.195 9.64 (J” = 3-f d+ 0.05 0.062 d,

‘) See ref. $)_ b, See ref. I’). “) See ref. Is). a) See ref. 19).

PROTON TRANSFER 397

I60 . . -+ “N+p and llBs,r++p -+ “C are summarized in tables 3 and 4 and com- par:; to the results of other reactions ‘* l8 - ’ “) and theoretical predictions I’).

In general the agreement is excellent at least for the higher energies. The absolute spectroscopic factors have the right order of magnitude, they are larger by a factor 1.5 as compared to the other analysis.

To demonstrate the energy dependence of the spectroscopic factors the values

02/#o McV are listed in table 5, showing that this value is unity within a few percent. Only for the lowest energies deviations are observed, probably due to the fact that for these energies the absolute cross section is more uncertain as pointed out earlier.

TABLE 4

Relative spectroscopic factors 6z/@S...2 for the transition i60g.1. --f lJN+p

Final state in “N

This experiment (d, ‘HeI ‘1 Thwry ~_. shell model

bound EM (MeW state

27 30 32.5 35 60

g.s. (J” = 4-1 P* I 1 1 1 I 1 1 6.33 (J” = $-) p+ OS 1.57 1.06 1.82 1.8 1.74 2

*) See ref. z”).

TABLE 5

Relative spectroscopic factors 8*/&, Mcv2 obtained by i1B(160, 1 sN)12C

Exy 8.s.. g.s. g.s., 4.44 6.33, gas.

60 1 1 1 35 0.99 1.1 1 32.5 1.02 1.1 0.6 30 0.7 1.1 0.64 27 1.3 1 0.35

4.3. *%Jt9F, **Ne)“B

A spectrum of the reaction *‘C( “F, 2 ‘Ne)’ 1 B is shown in fig. 11. Only the ground state, the 2+ level of “Ne at 1.63 MeV and the f- level of ‘tB at 2.12 MeV are ob- served with considerable cross section. The strong line at 3.8 MeV corresponds to the transition leaving both reaction products in their first excited states.

The angular distributions decrease to backward angles by a factor 103, indicating that contributions from compound-nuclear reactions and the competing seven- nucleon transfer are negligible. This is illustrated for the ground state transition in fig. X2, the other transitions show the same behaviour, however, the backward angles are omitted in figs. 13 and 14.

150 F”‘““‘“7 L f 8:” N

-I

9 (D In*: : 0 116

t 2 100 - 0

?!&dmNe

*-- e 0 ,I ‘*C(‘sFa 20Ne)“B

k ELsb = 68.8 MeV _

0 30 60 90

channel

Fig. 11. Energy spectrum of the p-transfer “C(‘9F, “Ne)’ ‘B.

Il”““““““‘l

66 6 UeV

60 uev

B 100 b t 1

. ,i t

: Pd

lo-’ t** ”

2 t 4 \ t

,-33 0’ 30” 60’ 90“ 120” 150’

8 cm.

‘2C(1gF.20N9~,~~~“6g.s. -

%nl.

Fig. 13. See caption Fig. 14. Fig. 12. See caption Fig. 14.

PROTON TRANSFER 399

lo-’

ELAN = 68.8 MeV

0" 30” 60” %.,.

Fig. 14. DWBA calculations for the angular distributions of the p-transfer 12C(19F, z”Ne)llB.

The DWBA description of the angular distributions are shown in figs. 12, 13 and 14, the parameters are summarized in table 6. For the 60 MeV data and the transition to the 2.12 MeV level at 68.8 MeV the parameters are exactly the same as those used for the description of the elastic scattering and about the same used for the p-transfer llB ( r60, 15NgS )“C. For the description of the other data the radii of the real . . potential were changed by 10 to 15 % in both channels but in the same way for all cases.

TABLE 6

Optical-model parameters for the DWBA description of the reaction 12C(lgF, aoNefllB (figs. 12, 13, 14)

Final f&t. Initial Final states (MeV)

(20Ne, ltB) (A) (A$ (fZ) (hz) (Lz) (2) (MY& (Z) (zl) (Z) (z) (2)

p.s., g.s. 68.8 100 1.29 0.48 30 1.26 0.26 100 1.37 0.48 30 1.26 0.26 60 1.19 27 1.19 27 40 1.29 2.5 1.37 25

1.63, g.s. 68.8 30 30 60 1.19 27 1.19 27 40 1.29 25 1.37 25

g.s., 2.12 68.8 1.19 30 1.19 30

400 U. C. SCHLOTTHAUER-VOOS et al.

TABLE 7

Relative spectroscopic factors f32/~r.,.2 for the transition “C,.,. --f “Bip

Final state in “B

Bound state

This experiment

(“B, ‘*C) ‘) (d, “He) ‘) Theory ‘)

g.s. (P = )-) Pt 1 1 1 1 2.12 (P = J-) p1 0.25 0.28 0.26 0.263

“) See ref. 5). b, See ref. 21). ‘) See ref I’) . .

TABLE 8

Relative spectroscopic factors O*/O,.,.z for the transition 19F,.,. +p + 20Ne

Final state in Z”Ne

This experiment (d, n) ‘) (3He, d) b, (CL, t) ‘) Theory d, -

bound EM (MeV) shell SU(3) state - -- ---- model

40 60 68.8

g.s. (P = o+) s+ 1 1 1 1 1 1 1 1 1.63 (J” = 2+) d+ 0.88 0.89 0.89 1.13 2.03 0.2 0.78 0.56

c ‘) See ref. 22). b, See ref. 23). ‘) See ref. 2s). d, See ref. 24).

The relative spectroscopic factors for the transition “Cp+ + “B+p are sum-

marized in table 7. They are in excellent agreement with other experiments ‘, “) and

the theoretical values 17).

For “Ne , different treatments of the bound state wave functions give different

spectroscopic factors (see table 8). Most authors used shell-model wave functions in

their DWBA analysis and in calculations of the spectroscopic factors 22-24). The

theoretical values ‘) and those obtained by (d, n) [ref. “)I are approximately the

same, whereas the (3He, d) relative spectroscopic factors 23) differ by a factor 2. The

SU(3) [ref. 24)] and the (a, t) [ref. ‘“)I va ues, where oscillator wave functions are 1

used, are remarkably smaller and take into account the deformation of “Ne.

We followed the simple procedure used in refs. 22-24), assuming shell-model wave

functions, that means for the “Ne ground state a 2s+ wave, for the 2+ state a Id,

configuration for the proton. Our spectroscopic factors (table 8) are similar to those

obtained by (d, n) [ref. “)I and in reasonable agreement with the theoretical shell-

model values 24).

5. Conclusions

For the first time a systematic DWBA analysis of proton-transfer reactions induced

by heavy ions is given. It could be shown that the concept of strong absorption, which

has been successfully applied to the description of the heavy-ion elastic scattering in

the forward hemisphere ’ O), gives also a reasonable procedure for one-nucleon heavy-

PROTON TRANSFER 401

ion transfer reactions. All the reactions shown here could be described in a con- sistent way over a wide range of energies by the optical-model parameters obtained from the elastic scattering (with sometimes only slight changes to improve the quality of the fit).

Furthermore it was shown that heavy-ion transfer reactions give relative spectro- scopic factors for single nucleons which are as reliable as those obtained by conven- tional reactions and independent of the incident energy.

Due to the use of strongly absorbing potentials the calculated cross sections are less sensitive to the details of the optical-model wave functions.

The authors wish to thank Dr. H. H. Gutbrod and K. D. Hildenbrand for their help during the measurements.

References

1) R. Bock, M. GroDe-Schulte and W. von Oertzen, Phys. Lett. 22 (1966) 456 2) W. von Oertzen, H. G. Bohlen, H. H. Gutbrod, K. D. Hildenbrand, U. C. Voos and R. Bock,

Proc. Int. Conf. on nuclear reactions induced by heavy ions (North-Holland, 1970) p. 156 3) P. H. Barker, A. Huber, H. Knoth, U. Matter and P. Marmier, Proc. Int. Conf. on nuclear

reactions induced by heavy ions (North-Holland, 1970) p. 152 4) W. von Oertzen, M. Liu, C. Caverzasio, J. C. Jacmart, F. Pougheon, M. Riou, J. C. Roynette

and C. Stephan, Nucl. Phys. Al43 (1970) 34 5) W. von Oertzen, H. H. Gutbrod, U. C. Voos and R. Bock, Nucl. Phys. Al33 (1969) 101 6) T. Kammuri and H. Yoshida, Nucl. Phys. Al29 (1969) 625 7) F. Schmittroth and W. Tobocman, Phys. Rev. 1C (1970) 377 8) P. J. A. Buttle and L. J. B. Goldfarb, Nucl. Phys. 78 (1966) 409; Nucl. Phys. All5 (1968) 461 9) A. Dar, private communication

10) U. C. Voos, W. von Oertzen and R. Bock, Nucl. Phys. A135 (1969) 207 11) R. Bock, M. GroOe-Schulte and W. von Oertzen, Phys. Lett. 22 (1966) 456 12) W. R. Gibbs, V. A. Madsen, J. A. Miller, W. Tobocman, E. C. Cox and L. Mowry, NASA TN

D-2170 (1964) 13) R. H. Bassel, R. M. Drisko and G. R. Satchler, ORNL 3240 (1962) 14) F. G. Perey, Optical-model program JIB 3 15) W. von Oertzen, H. H. Gutbrod, M. Miiller, U. C. Voos and R. Bock, Phys. Lett. 26B (1968) 291 16) D. Robson, Contribution to the symposium on heavy-ion scattering, Argonne, 1971 17) S. Cohen and D. Kurath, Nucl. Phys. Al01 (1967) 1 18) W. Bohne, H. Homeyer, H. Morgenstem and J. Scheer, Nucl. Phys. All5 (1968) 457 19) P. D. Miller, W. R. Coker and Jung Liu, Nucl. Phys. Al36 (1969) 229 20) J. C. Hiebert, E. Newman and R. H. Bassel, Phys. Rev. 154 (1967) 898 21) F. Hinterberger, G. Mairle, U. Schmidt-Rohr, P. Turek and G. J. Wagner, Nucl. Phys. A106

(1968) 161 22) R. H. Siemssen, R. Felst, M. Cosack and J. L. Weil, Nucl. Phys. 52 (1964) 273 23) R. H. Siemssen, L. L. Lee Jr. and D. Cline, Phys. Rev. 14OB (1965) 1258 24) T. Inoue, T. Sebe and H. Hagiwara, Nucl. Phys. 25 (1966) 184 25) L. F. Hansen, H. F. Lutz, M. L. Stells, J. G. Vidal and J. J. Wesolowski, Phys. Rev. 158

(1968) 917