16O-INDUCED TRANSFER REACTIONS IN THE f-p SHELL

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16O-INDUCED TRANSFER REACTIONS IN THE f-p SHELL

G. Morrison

To cite this version:

G. Morrison. 16O-INDUCED TRANSFER REACTIONS IN THE f-p SHELL. Journal de Physique Colloques, 1971, 32 (C6), pp.C6-69-C6-81. �10.1051/jphyscol:1971610�. �jpa-00214828�

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JOURNAL DE PHYSIQUE Colloque C6, supplkntent au no 1 1-12, Tome 32, Novembre-De'cembre 1971, page C6-69

160-INDUCED TRANSFER REACTIONS IN THE f-p SHELL (*)

G . C. MORRISON

Argonne National Laboratory, Argonne, USA

Rhume. - Une etude systematique des reactions de transfert induites par des ions ^{1 6 0}dans une large skrie de noyaux de la couche f-p, du 4oCa au 7oZn, a Bte faite B une energie incidente de 48 MeV. Les principales reactions observkes sont (160, lsN), (160, 14C) et (160, I T ) . Leur nature directe a Cte mise en evidence en etudiant la variation systematique des distributions angu- laires avec Q , Z e t B. Les resultats des calculs bases sur I'approximation de Born avec ondes defor- mCes et portee finie pour la reaction (160, IsN) seront presentb, et le r61e trQ important du moment angulaire dans la dynamique des reactions induites par ions lourds sera mis en evidence.

Abstract. - A systematic investigation of 160-induced transfer reactions on a wide range of fp-shell target nuclei from 4oCa to 7oZn has been performed, mainly at a bombarding energy of ⁴⁸MeV. The principal reactions observed are (160, lsN), (160, 14C) and (160, 12C), their direct nature being found in the systematic variation of the angular distributions with Q , Z and E.

The results of finite-range DWBA calculations for the (160, IsN) reaction will be presented, and the very important role of angular momentum in heavy-ion reaction dynamics will be made explicit.

1. Introduction. - During the past few years an increasing fraction of nuclear-reaction studies on tandem Van de Graaffs has involved the use of heavy ions as projectiles. While this trend has been stimulated by continuing improvements in the intensity and variety of the heavy-ion beams available and by the development of refined detection techniques, the increasing use of heavy ions primarily reflects an increasing awareness that the interaction of complex nuclei focuses on several new and exciting areas that are inaccessible to the more conventional light ions.

Although systematic studies of the elastic scattering of heavy ions have been pursued for some time, it is now realized that there is a need to expand our picture of the interaction obtained from scattering studies. In particular, it is of interest to determine the relative importance of the closely related phenomena of transfer reactions wherein the two colliding nuclei are little disturbed -reactions in which only one or a few nucleons are transferred to or from the target nucleus in a close collision.

In the work reported here, fp-shell target nuclei in the wide range from 40Ca t o 'OZn were bombarded with 160, usually at 48 MeV. This incident energy was selected because it is sufficiently above the Coulomb barrier for the cross sections to be appreciable and still near enough the barrier for the reaction mechanism to be simple in that the nuclear trajectories are approximately classical (the Sommerfeld parameter ^q²¹15 for

(*) Work performed under the auspices of the U. S. Atomic

Energy Con~mission.

48 MeV ¹⁶⁰ions incident on 40Ca). The decision to study the resulting transfer reactions for a wide range of targets at the same incident energy was made in the hope of obtaining information on their systematic dependence on the mass and charge of the target nucleus and on the Q value of the reaction. The aim was twofold, namely (1) to compare heavy-ion and light- ion transfer reactions in order to distinguish aspects in which they differ (such as the possibility that excitations in entrance and exit channels might be of greater importance for heavy-ion reactions) and (2) to use several-nucleon transfer to examine few-nucleon corre- lations and clustering in the residual nuclei.

Although the 160 projectile was initially adopted for a study of a-particle transfer by means of the (160, 12C) reaction, this paper will be primarily directed towards an understanding of the mechanism of the ¹⁶⁰induced transfer reaction. To this end it will deal primarily with our observation and exploitation of the simpler one- and two-proton transfer reactions, namely (160, 15N) and (160, 14C) which may be compared with the corresponding light-ion reactions (3He, d) and (jHe, n).

This comparison points up some of the novel features of the heavy-ion reactions. In what follows, a selection of the results, mainly those for calcium isotopic targets, will first be presented and a qualitative classical interpretation of their systematic features will be given.

Next the experimental results on the (160, 15N) reaction will be compared with some preliminary DWBA calculations. And finally the important role of angular momentum in heavy-ion transfer reactions will be explicitly discussed.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971610

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2. Survey of experimental data and their classical interpretation. - In these experiments (carried out in collaboration with H. J. Korner, L. R. Greenwood and R. H. Siemssen) 160 beams from the Argonne tandem Van de Graaff were incident on enriched isotopic targets 50-100 pg thick in the 70-in. scattering chamber.

The outgoing particles were detected in four (dE/dx).E counter telescopes mounted at 100 intervals on one of the computer-controlled arms of the scattering chamber. To achieve mass separation, coincident dE/dx and E signals were summed and multiplied for each individual telescope. The resultant mass and energy signals were routed to and directly stored in four two- parameter arrays of 8 192 channels each in the large external memory associated with the ASI-210 computer. An example of the energy resolution and mass separation achieved is shown in figure 1. The some-

...

;;so

?.--0

ZOO I I

FIG. 1. - Energy and mass spectra from the bombardment of 64Ni with ^{1 6 0}ions a t an incident energy of 48 MeV. Slices of the two-dimensional coincidence spectra are projected onto the energy (E + AE) and mass (E x A E ) axes, respectively. The mass spectrum shows a clear separation between 12C and 14C ; the corresponding energy spectra obtained by setting mass win- dows with a light pen on the I2C and 14C are shown on the left.

what poor energy resolution (200-300 keV) primarily reflects the greatly increased sensitivity of heavy-ion reactions to target thickness and kinematic spread. The three mass groups in the spectrum at the right correspond to 12C, I4C and 15N and represent the predo- minant heavy-ion reaction products from ¹⁶⁰bombardment.

a) THE SINGLE-PROTON TRANSFER REACTION (160, I5N). - Figure 2 shows spectra from the (160, I 5 N )

reactions on the even-A calcium isotopes from 40Ca to 48Ca. In each case, E(160) = 48 MeV. The final states observed in the Sc isotopes are just those states that had previously been observed to be strong in the (3He, d) reaction. The ground states (Jn = 712-) all represent 1 = 3 transitions ; the excited states are mainly (J" = 312-) 1 = 1 transitions. Figure 3 shows the angular distributions of the 1 = 3 ground-state and a prominent I = 1 excited-state transition at

~ ( ' ~ 0 ) ⁼48 MeV for each of the Sc final nuclei.

16 15 Ca( 0 , NISc

~ ( ' ~ 0 ) = 48 MeV

3 0 60 90 C H A N N E L N U M B E R

FIG. 2. - Energy spectra of the (160, IsN) reaction on the even-A Ca isotopes a t E(160) = 48 MeV.

Figure 4 shows the angular distributions for 4 9 S ~ at E(160) = 42, 48 and 56 MeV.

The simple shapes of the angular distributions, their insensitivity to transferred I, and the shift in peak position as a function of Q value and bombarding

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'60-INDUCED TRANSFER REACTIONS IN THE f-p SHELL C6-71

energy can be given a simple qualitative interpretation.

Based on the classical Coulomb trajectories of the colliding ions, there is a unique relation between scattering angle and the distance of closest approach, namely,

where b is the distance of closest approach in a head-on collision. The more forward angles represent those collisions in which the nuclei come less close together so there is little overlap and hence only a small transfer cross section. Increasingly large angles correspond to closer and closer collisions. Hence thc transfer cross section increases with angle until it peaks as the overlap reaches its maximum at the angle corresponding to a contact collision -the grazing angle -independent of the transferred I. At still more backward angles (still closer collisions) the cross section decreases as absorption processes predominate over the simple transfer process.

On the basis of the classical relation (I), one also predicts that the transfer reaction peaks at more backward angles for lower incident energies and more negative reaction Q value (Figs. 3 and 4). It is also

FIG. 3. - Angular distributions of the (160, 15N) reaction on the even-A Ca isotopes leading to the J n = 712- ground state (I = 3) and to a prominent Jn := 312- excited state (I = 1 ) in

cach of the Sc final nuclei ; E(160) = 48 MeV.

predicted, and is indeed found (Fig. 5), that the peak angle moves back with increasing Z of the target nucleus.

Another characteristic observed thro~ighout the energy range studied is that the peak cross section for a fixed Q value is only slightly dependent on the incident cnergy - as is observed for 48Ca in figure 4. This behaviour at energies above the Coulomb barrier agrees with the classical expectation that at energies high enough to attain a contact collision, the maximum cross section associated with this interaction radius is nearly independent of energy. However, as can also bc

, 1- - , ^- ⁷ ^- ¹ - ¹ ^, i 1 - - - , . ^I

i 4 8 ~ a ( 1 6 ~ . ' 5 ~ ) 4 9 ~ c E,=O

I O F 1 E,=3.08 M e V j

48 M e V

-'\ ^11,

5 6 MeV

\

C.M. A N G L E

FIG. 4. - Angular distributions of the 4*Ca(160, 15N)49Sc reaction to the final states shown for E(160) = 42,48 and 56 MeV.

FIG. 5. - Angular distributions of thc (160, IsN) reaction for 1 - ³ ^and¹ transitions to the indicated final nuclei ;

E(160) = 48 MeV.

seen in figures 2 and 3, the magnitude of the peak cross section does depend strongly on the Q value of the reaction : the more negative the Q value the smaller the cross section. It will be shown later that this reduction results mainly from the severe momentum mismatch in the entrance and exit channels at very negative Q values (which increases the importance of the Coulomb barrier). Such a mismatch is also expected for very positive Q values.

The grazing distance of closest approach was calculated from the peak angles in the angular distributions of the Ca(160, ^15N)reaction by matching the

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C6-72 G . C. MORRISON

separate trajectories for the 160 and "N ions.

Although the resulting interaction radii varied systema- tically with target A, the value of r,, where

was unrealistically large - around 2.0 F. It may be inferred from this result that effects of nuclear distor- tions are important even at these relatively low bom- bard~ng energies. Because of the attractive nuclear forces, such distortionc in the ingoing and outgoing channels lead to a forward focusing of the angular distribution ; and this focusing is reflected in the large apparent value of the interaction radius computed on the simple classical picture. However, it should also be noted that acceptable values of r, (z 1 . 5 F) have been consistently derived from classical analyses of the angular distributions of neutron-transfer reactions both above and below the Coulomb barrier - an apparent paradox not understood at present. Attempts to fit the observed angular distributions with a full DWBA treatment will be described in section 3.

The results of these (160, ' 'N) experiments on the Ca isotopes give no evidence that the proton-transfer reaction has any peculiar aspect unique to heavy-ion reactions. When the observed peak cross sections for (160, "N) reactions to individual levels are divided by the corresponding proton spectroscopic strengths derived from thc (3He, d) reaction, the resulting normalized (160, lSN) cross sections for 1 = 3 and I = 1 proton transfers vary smoothly as a function of Q.

Furthermore, the only states seen in the (I%, 15N) reaction are those that are also excited in the (3He, d) reaction.

For targets other than Ca, however, the situation changes -especially for nuclei in those regions of A for which collective effects are known to be present. For such target nuclei (e. g., for ''Ti, 62Ni and 64Ni), some of the observed states correspond to protons coupled to excited-core configurations of the target and do not correlate with the states observed in simple proton transfer by the (3He, d) reaction. This difference in the intensity of the states observed in the two reactions is an effect to be expected if the probability for inelastic excitations in both the entrance and the exit channel is much higher for heavy ions than for light ions.

A particularly striking case is found in the spectrum of the 50Ti(160, l s N ) s l V reaction shown in figure 6.

Quite clearly seen is the 1112- state at 1.61 MeV in "V.

This state is a member of the multiplet based on an effective (f,,, ^@2 + ) configuration and is unobserved in the (3He, d) reaction. However, an apparent puzzle still exists in that the 912- member of the multiplet which occurs at 1.8 1 MeV is still unobserved (or very weak) in the (160, I5N) reaction. (The 3/2- member at 0.93 MeV is weakly seen, while the 512- member at 0.32 MeV is unresolved from the 51V ground state.) Its resolution requires more detailed considerat~on of the two-step process in transfer reactions.

C H A N N E L N U M B E R

FIG. ^6.- Energy spectra of the suTi(l60, 15N)51V reaction at E(160) - 48 MeV showing the excitation of the 1112- state at 1.61 MeV. The lower curve represents a very recent run in which considerably improved rcsolution was achieved at the

expense of solid angle.

The two-step process involves two coherent paths, namely inelastic excitation in the entrance channel followed by transfer and transfer, followed by inelastic excitation in the exit channel. This is shown schematically in figure 7. For the case of an even-A target (Ji = O),

FIG. 7. - Schematic representation of the two-step process in a stripping reaction showing the two possible paths that

contribute coherently [ref. 11.

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'"-INDUCED TRANSFER REACTIONS IN THE f-p SHELL C6-73

the matrix element reduces to the form shown [I]. Then the changing sign of the phase factor ( - l ) r 1 + 1 2 + J f

leads to alternate enhancement and inhibition of transitions to multiplet members of successive J , , with J , = J,,, being enhanced. The effect will be greatest when the probabilities for inelastic excitation in the two paths are approximately equal - a situation which should be most nearly satisfied in heavy-ion transfer reactions. Thus the observation of this effect in 5 0 ~ i ( ' 6 0 , 5N) would seem to provide striking confir- mation of the importance of the two-step process in the heavy-ion reaction.

No other such clear example has been found in the present work. In heavier targets (such as 6 2 . 6 4 ~ i ) while some of the states observed in the (160, "N) reaction do not correlate with those observed in the (3He, d) reaction, the lack of experimental resolution (as can be

CHANNELS

FIG. 8. - Energy spectra of the (160, IsN) reaction on 62Ni, 6JNi and 7oZn targets at E(160) = 48 MeV. The inadequacy

of thc usual experimental resolution is now apparent.

seen in Fig. 8) is a fundamental limitation and precludes a detailed analysis. Thus, although the role of heavy-ion proton-transfer reactions appears an exciting prospect in studying the importance of proton coupled to excited-core configurations, detailed information can come only from experiments performed with considerably improved resolution.

16 14

Ca( 0, C ) T i

m

9 ~ ( ' ~ 0 ) = 48 MeV

20 -

I 8,=33"

30 60 90

C H A N N E L N U M B E R

FIG. 9. - Energy spectra of the (160, 14C) reaction on the even-A Ca isotopes (masses 42-18) at E(l60) = 48 MeV.

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C6-74 G . C . MORRISON b) THE TWO-PROTON TRANSFER REACTION (I%, 14C).

-The reaction (160, 14C) also appears to proceed directly with transfer of two protons, and presents even clearer evidence of the heavy-ion nature of the ^160- induced transfer reactions. Two-proton-transfer data on the comparable light-ion (3He, n) reaction are scarce because of the inherent difficulties of neutron detection.

However, data on the analogous two-neutron-transfer (t, p) reaction on even-even nuclei are available for comparison. A prominent feature in the spectrum of the latter reaction is the mainly strong excitation of the 0' ground state relative to other excited states, but no such preferential excitation is found for the (160, 14C) reaction on the even Ca isotopes - as can be seen from figure 9. By contrast, in all cases studied, states strongly excited in the transfer reaction are also strongly excited in inelastic scattering. The fact that excitation of low-lying excited states is comparable to the ground state may reflect the possibility of excitation in the ingoing and outgoing channels, as in the case of the (160, ^{1 5 N )}reaction ; but also sequential transfer of protons in a heavy-ion collision may become more important and thereby favor states of higher spin.

However, angular-momentum effects are also of vary- ing importance over the wide range of Q values involved.

The shapes of the angular distributions for the (160, 14C) reaction are similar to those for the (160, 15w reaction, For each reaction, there is again a

~ a ( ' ~ 0 . I 4 c ) ~ i

E=48 MeV

FIG. 10. - Angular distributions of the ( ' 6 0 , 14C) reaction on the even-A Ca isotopes (masses 42-48) leading to the ground state ( 0 + ) and first excited state (2+) in each of the Ti final

nuclei ; E(160) = 48 MeV.

unique maximum which shifts to more back angles as the Q value of the reaction decreases (Fig. lo), as the incident energy decreases (Fig. 1 I), and as the Z of the target nucleus increases (Fig. 12). The increased breadth of the angular distributions compared to the corresponding (160, 15N) reaction may be associated with a less well defined grazing trajectory in the transfer of two particles. However, the angular distribution for

I ^{42 MeV}

FIG. 1 1 . - Angular distributions of the 48Ca(160, 14C)SOTi reaction to the final states shown for E(l60) = 42 and 48 MeV.

FIG. 12. - Angular distributions of various (160, 14C) reac- tions for ground state ( L = 0 ) and first excited statc ( L = 2)

transitions ; E(160) = 48 MeV.

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160-INDUCED TRANSFER REACTIONS IN THE f-p SHELL C6-75

two-proton transfer is more forward peaked and the maximum cross section is an order of magnitude smaller than that for the corresponding one-proton transfer reaction.

CHANNELS 80-

60

FIG. 13. - Energy spectra of the (160, 14C) reaction on 58Fe, 64Ni and 702x1 targets at E(l6O) = 48 MeV.

16 14 60

" ~ e ( 0 , C) Ni E (160) = 48 MeV

8,. 45" 5!

- ⁱ

I 2

N

On the basis of classical Coulomb trajectories, the more forward-peaked angular distributions imply a larger interaction radius for the (160, 14C) than for the (160, I5N) reaction - but this would seem unrealistic in view of the larger mass transferred in the former. If, on the other hand, two-nucleon transfer requires closer contact than one-nucleon transfer, the effects of nuclear distortion should be even more important. Then the increased focusing by the distorting potentials could result in a more forward-peaked angular distribution and the stronger absorption would lead to a smaller cross section than is the case for the (160, 1 5 N ) reac-

40 - ^'?

20 ^-

* ,

, ^I I I

tion. Indeed, the 4 8 ~ a ( ' 6 0 , 14C) angular distribution at the highest energies studied gives some evidence of an oscillatory pattern indicative of the increasing role of nuclear interactions. However, as will be seen later, preliminary DWBA calculations do not appear to predict peaking at angles as far forward as is observed.

When considering the variation in intensity of the (160, I4C) reaction from one target nucleus to another, there are no corresponding (3He, n) data to permit a separation of the nuclear-structure effects from the heavy-ion aspects of the reaction. The observed strong dependence of the peak cross section on Q value (and target Z ) again reflects the importance of Coulomb barrier and momentum mismatch for very negative Q values. (Indeed momentum matching considerations imply that, because of the very different Q values of the (160, 14C) and (3He, n) reactions, comparison of the two reactions on the same target may be less meaning- ful.)

In addition to these kinematic dependences, it is found that the probability for transferring two protons is strongly influenced by the details of the proton configurations in the target and final nuclei. This is exem- plified in figure 13 wherein the increased ground-state intensity of the ("%I, 14C) reaction on 64Ni compared with 58Fe presumably reflects the onset of filling of the 2 p3/, proton orbital. That the 2+ state is also relatively stronger on 6 4 ~ i may again indicate the importance of two-step processes in a region where collective effects are important. A further feature of the spectra shown in figure 13 is the relatively strong excitation of the collective 3 - state in each case. A summary of peak cross sections for excitation of the ground ( 0 + ) and first excited (2+) states for a range of nuclei is shown in figure 14. The trend of ground-state excitations reflects not only kinematic dependences (as seen for different isotopes) but also nuclear-structure effects, such as the

TARGET NUCLEUS

FIG. 14. - Summary of the peak cross sections for the (160, 14C) reaction on target nuclei ranging from 42Ca to 70Zn at E(160) = 48 MeV. The heights of the open and dashed vertical bars represent the cross sections for populating the

ground and first excited states, respectively.

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C6-76 G . C. MORRISON

I r in this almost completely unexplored area of nuclear

CHANNELS

FIG. IS. - Energy spectra of the (160, ^12C)reaction on the even-A Ca isotopes -at E(160) ²48 MeV. The shaded peak

represents the elastic recoil, of the 12C impurity.

filling of the I f l I z and 2 p,,, proton orbitals (as seen for different 2). For this reason, use of the (160, 14C) reaction holds promise as a unique spectroscopic probe

structure.

C ) THE a-PARTICLE TRANSFER REACTION (160, 12C).

-The (160, 12C) reaction also appears to proceed directly, in this case, with the transfer of an alpha-like four-nucleon cluster-though the mechanism of this reaction is the least well understood of all the reactions studied. In contrast to one- and two-proton transfer, the (160, 12C) reaction is observed to be strongest for target nuclei having the least neutron excess. This is evident in the Ca(I60, 12C)Ti spectra shown in figure 15.

The decrease in the population of low-lying excited states with increasing neutron excess can be given a qualitative structure explanation (e. g., in the paper by Arima). However, changes in Q value with increasing neutron excess result in an increased angular momentum mismatch for these low-lying states - an effect which must also be taken into account.

Since for all but a few target nuclei, such as 40Ca, the cross section for excitation of individual low-lying excited states by four-nucleon transfer is much smaller than in one- and two-proton transfer reactions, angular-distribution data are much harder to obtain. In those cases measured, they are again susceptible t o a direct-interaction interpretation in their dependence on Q and 2, and continue the trend observed in going from one- to two-proton transfer : the angular distributions are broader, the forward peaking increases, and the peak cross section decreases as the number of transferred particles increases. This is evident in the 40Ca angular distributions shown i n figure 16, where there is some evidence also for the onset of an oscillatory pattern at 48 MeV. Unfortunately, the present experiment iseffec- tively limited to the most forward angles shown.

However, the greatest intrinsic interest in the (160, I 2 c ) reaction is perhaps in connection with cur- rent theoretical speculation concerning the existence of alpha-like quartet states in nuclei. A comparison of the spectra from (160, I2C) and (160, 14C) reactions to the same final nucleus shows considerable differences. This is seen in figure 17, which compares the spectra for these two reactions leading to the residual nucleus 66Zn. Up to a few MeV excitation in this and the other cases studied, states that are strongly excited in two- proton transfer are only weakly excited in the (160, ',c) spectrum. At higher excitation energies, on the other hand, the (160, 12C) spectrum shows strong isolated structure whereas the two-proton transfer shows little peaking.

The increased strength of the (160, 12C) reaction to states at higher excitation energies appears to give qualitative support to the expectations of the quartet model. However, by aligning the (160, 12C) and (160, 14c) spectra with excitation energy as in figure 17, the difference in Q values of the two rcactions (- 2.6 and - 6.0 MeV, respectively) is obscured. As will be seen later (Fig. 25), the Q value in both reactions for optimum angular-momentum matching is around

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160-INDUCED TRANSFER REACTIONS IN T H E f-p SHELL '26-77

4 0 ~ a ( ' 6 ~ . ' 2 ~ 4 4 ~ ~

E . 4 2 M e V E m 4 8 MeV

C

. -.- ^..

,.' i.' _+..

*. ^'^+, ^1.09

2.50

..- A-.

3.35

FIG. 16. ---. Angular distributions of the 40Ca(lW0, 12C)44Ti rcaction to the final states shown for E(160) = 42 and 48 MeV.

-7.0 MeV, so that kinematic effects contribute impor- tantly to the shape of the spectra and may largely exaggerate the diffcrent selectivity of the two reactions.

A further point t o be noted in figure 17 is that the 3 - state at 2.83 MeV appears excited in both reactions, although its observation in the (160, lZC) reaction is inconsistent with the simple stretch scheme for quartet states. Nevertheless, the fact remains that the (I", 12C) reaction appears to populate only selected states (or groups of states) at high excitation energies, and is perhaps the best evidence for alpha-like configurations in these nuclei. Most important for a detailed analysis of such structures would be a high resolution study of the (160, 12C) rcaction.

3. DWBA calculation of heavy-ion transfer reactions.

- This 'section describes some initial attempts to calculate angular distributions of 160-induced transfer reactions with a DWBA treatment. The calculations utilize the program RDRC of Schmittroth and Toboc- man [2], which treats the finite-range problem by expanding the bound-state Woods-Saxon wave functions of the transferred particle in terms of harmonic- oscillator wave functions. Thus, except for the neglect of certain recoil effects, the calculations are exact within the framework of a DWBA theory.

At this time, the DWBA calculations have been

62 16 12 66

N i ( 0 , C ) Zn

~ ( ' ~ 0 ) = 48 MeV

Lo

20 50 80 ^{I ~ O} C H A N N E L N U M B E R

FIG. 17. - Intercomparison of the spectra from the 62Ni(160, 12C) and 64Ni(160, 14C) reactions leading to the same residual

nuclcus 66Zn. E(160) = 48 MeV.

performed mainly for the (160, 1 5 ~ ) one-proton transfer reactions on the Ca isotopes. In these initial calculations, ⁽⁽strongly ⁾⁾absorbing heavy-ion optical potentials were chosen since these obviate the need for a cut-off radius and are less critical to .use than the alternative cr weakly ^Dabsorbing potentials found in heavy-ion scattering on light nuclei [3]. The potential parameters are given in table I. Those for 160 give an excellent fit to 48Ca + ¹⁶⁰scattering data ; those for 15N were arbitrarily chosen the same except for the diffuseness. The larger diffuseness chosen has no a priori justification except that it was found necessary in order to fit the position of the peak in the 48Ca(160, 15N) angular distributions. (The peak in the calculated angular distribution shifts to forward angles with increasing diffuseness.) The bound state parameters are those chosen by Bassel et aI. [4] for (3He, d) and (d, 3He) DWBA calculations.

Optical-Model and Bound-State Parameters

V W Yo a

[MeV] [MeV]

- [Fl [Fl

- -

1 6 0 100 40 1.22 0.49

15N 100 40 1.22 0.60

B. W. 1.20 0.65

R = r o ( ~ ; l 3 + A : ' ~ )

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C6-78 G . C. MORRISON

The calculated 1 = I and 1 = 3 angular distributions for 48Ca(160, 15N) at three different energies are compared with experiment in figure 18. The quality of

-4G60.'d)J)49si ^a ^' ^' 1

5,6

?

MeV ^{= 3} 48 M e V

A

Ex=3.08 M e V

56 MeV

, i

^{' = I}

l

4 8 MeV

C.M. ANGLE

FIG. 18. - DWBA fits to the 48Ca('60, ISN)49Sc angular distributions shown in figure 4. The normalization differs for the two final states but is the same at each bombarding energy.

the overall fit is extremely good, both in shape (even to the onset of oscillations at 56 MeV) and relative magnitude (since the DWBA curves have the same rela- tive normalizations at each energy). In principle, the ratio of experimental to calculated DWBA cross sec- tion gives directly the product of the spectroscopic factors of the transferred particle in the projectile and final nucleus. In practice, however, we express

where the normalization factor N is introduced to measure the success of the DWBA calculation. The spectroscopic factors S, and S, refer to the projectile and residual nucleus ; for the (160, 15N) reaction, S , = 2.

Figure 19 shows the DWBA fit to the Ca(160, I5N) reactions at 48 MeV. The parameters are those given in table I, in which only R varies with A . Although the overall agreement appears reasonable, the calculated distributions fail to reproduce the experimental peak positions for the most negative Q values. The trend is shown more clearly in figure 20. Since the sensitivity of the calculated angular distributions to the details of the nuclear surface should be most acute for large momentum mismatch, the observed disagreement is perhaps not unexpected and may even suggest the possibility of extracting detailed information on the nuclear surface in these cases. Figure 20 also shows the comparative insensitivity of the peak position to transferred I. Of course, this apparent lack of uniqueness in the shape of the angular distributions precludes their utilization to

FIG. 19. - DWBA fits to the experimental Ca(160, 15N)Sc angular distributions shown in figure 3.

-I I -9 -7 -5 -3

0 - V A L U E ( M e V )

FIG. 20. - Conlparison of the position of the peak in the Ca(160, I5N)Sc angular distributions with DWBA predictions.

determine the transferred angular momentum in a way familiar in light-ion transfer reactions - at least at for heavy ions a t incident energies close to the Coulomb barrier.

The quotient obtained when the observed Ca(160, 15N) peak cross sections to individual levels divided by the corresponding proton spectroscopic strengths derived from the (3He, d) reaction may also be compa- red directly with the calculated DWBA cross sections.

Figure 21 shows that the extremely strong Q dependence of the experimentally observed values (ranging over two orders of magnitude) are well reproduced by the cafculated 1 = 1 and 3 transfer cross sections. This comparison gives an overall normalization close to unity (N z 1.5). The possibility that transferred I values may be determined from differences in excitation functions as in sub-Coulomb stripping is also suggested from the results shown in figure 21.

The spectroscopic factors obtained from the (160, 15N) reaction with the normalization N - ^,^1.5are

directly compared with those from the corresponding (3He, d) reaction in figure 22 in order to illustrate the range of spectroscopic values for which agreement is

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160-INDUCED TRANSFER REACTIONS IN THE f-p SHELL C6-79

0 - V A L U E ( M e V )

FIG. 21. - Comparison between the peak cross sections of the between Ca(160, 1SN)Sc reactions divided by the corresponding ('He, d) spectroscopic factors and DWBA predictions. The fit

gives the normalization factor N = 1.5.

observed. At this preliminary stage no attempt has been made to vary the bound-state parameters, although it is to be expected that N is sensitive to the values chosen.

T A R G E T NUCLEUS

FIG. 22. - Comparison of (160, IsN) and ('He, d) spectroscopic factors for 1 f7/2 and 2 p,,z proton transfer on the even-A Ca

isotopes.

Finally, in a spirit of exploration, DWBA calculations were extended to heavier nuclei using still the parameters of table I and allowing only R to vary with target A. Figure 23 compares the calculated angular distributions with the experimental data for '*Fe and 6 4 ~ i ( ' 6 0 , lSN-) reactions. The observed good fit to the angular distributions extends also to the spectroscopic factors determined with the same normalization (N z 1.5) as before. For 5 8 ~ e , a spectroscopic factor of 0.28 from the (160, 15N) reaction compares with that of 0.17 from the (3He, d) reaction ; for 6 4 ~ i , the corresponding values are 0.81 and 0.80, respectively ! Although an exhaustive search to determine the sensitivity of the DWBA cross sections to the distorting and

FIG. 23. - DWBA fits to the experimental 58Fe(160, 1sN)sYCo and 64N(160,lsN)'jsCu angular distributions shown in

figure 5.

bound-state parameters has not yet been performed, the successful description of this wide range of experimental data with a fixed set of parameters presumably reflects the importance of the Coulomb field and surface localization in the heavy-ion transfer reaction at these bombarding energies.

Attempts to calculate 160-induced two-proton and alpha transfer with the RDRC program are still at a very preliminary stage. However, the initial calculations d o not appear to predict peaking at angles as far forward as is observed experimentally, but rather give peak positions similar to those found for one-proton transfer. Such an observation if it persists may arise from the neglect of recoil effects in the present DWBA calculations. While recoil effects certainly increase in importance as the number of transferred nucleons increases, their effect on the position of the peak in the angular distributions is not clear - although their inclusion may help to explain the increased broadening that is observed. It should also be pointed out that the calculations predict that the angular distributions rise again at forward angles beyond the range of the present experimental results - a result perhaps remi- niscent of the qualitative predictions of the semi- classical model of grazing collisions [5]. Clearly more study, both experimental and theoretical, is necessary.

4. Reaction dynamics. - In this final section I would like to make explicit the role of angular momentum in determining the dynamics of the transfer cross sections - a role which has been implicit in the discus- sion until now. In particular, the effects of momentum mismatch can be considerably more severe for heavy

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C6-80 G. C. MORRISON

ions than for light ions because of the high angular momentum associated with the heavy-ion channel and the sharp surface localization of the reaction. This fact is reflected in the marked Q dependence of the reactions which has been observed.

The angular momentum L at the nuclear surface associated with a specific heavy-ion channel can be calculated from the classical formula

to achieve matching, either the reaction will be attenua- ted by the Coulomb barrier (AL = - ve) or will take place far out with little overlap (AL = + ve). The former situation holds for the 40Ca('60, "N)~'SC reaction, for example. It should also be noted that the form of eq. (4) ensures that the mismatch condition changes only slowly with bombarding energy, although at higher energies the localization restriction should become less important also.

A plot such as that shown in figure 24 for the Ca isotopes obviously can easily be modified to show the where K, R are as usual and r] is the Sommerfeld para- variation of L with Q value. In this way the separate meter. (For light ions + 0 and the more familiar curves for each isotope for a specific exit channel may expression is realized.) Calculated values of the grazing be reduced to a universal curve for that channel. For angular momentum for various possible reaction the transfer reaction defined by an entrance and specific channels that result from the ^{1 6 0}reaction on the exit channel, the Q value for which AL = 0 may be even-A calcium isotopes at an incident energy of determined for a given target Z by use of eq. (4) ; and, 48 MeV are plotted in figure 24 for different excitation as discussed above, for that value of Q = Q,,, the transfer is favored for all values of 1. It can also be

E (160) a 4 8 MeV

1 ' 1 ' I ' ' I . , ' ' 1 . 1 ' ' l 8 l V '

40 42 44 4 6

Ca

Co Co Co ⁴⁸Co

20 -

F I G . 24. - Calculated values of the grazing angular momentum for various reaction channels which result from 1 6 0 bom- bardment of the even-A C a isotopes at 48 MeV. Thc abscissa

is the excitation energy in the reaction channels.

energies Ex in the reaction channels. (In actual practice, transmission factors were obtained from optical-model calculations for the various reaction channels and the value of L at the nuclear surface was defined as that L for which T,, = 1/2.) As was anticipated, it can be scen that L varies rapidly with Ex, changing by approxima- tely 1 unit per I MeV.

For a specific transfer reaction the transferred 1 value that is most favored may be determined for different excitation energies from the difference in L (= L, - Li) between the exit and entrance channel - the momentum mismatch. When the momentum is the same in both entrance and exit channels (AL = O), I = 0 transfer is favored although this matched condition serves to optimize thc reaction for all transferred I.

When the two channels differ greatly in L, a small transfer cross section should result since, in attempting

shown that Q,,, defined in this way is in essence the same as that introduced by Winther [6] to correct the actual Q value for the difference in Coulomb energies in the entrance and exit channels. At energies below the barrier, the same matching condition leads to the Goldfarb approximation [7] which obtains Q,,, by setting q i = r],.

Figure 25 shows a plot of the optimum Q values for j60-induced one- and two-proton stripping reactions as

Ud

20 3 0 4 0

T A R G E T Z

FIG. 25. Optimum Q values for the (160,lsN) and (160, 14~12C) reactions as a function of target Z.

a function of target Zfor an incident energy of 48 MeV.

The sign of Q,,, is negatives ince thechange in Coulomb energy is positive for such reactions. (The plots for the corresponding one- and two-protons pick-up reactions are similar except that the sign of the ordinate scale is reversed.) At Q = Q,,,, all transferred 1 are matched ; as Q deviates from Q,,, mismatch ensues, the low 1 values being most rapidly affected (simply from consideration of angular-momentum coupling). This feature of the matching is illustrated in figure 26,