PRESENT STATE OF EXPERIMENTAL RESULTS OF DIRECT REACTIONS WITH EMPHASIS ON NUCLEAR STRUCTURE INFORMATION

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PRESENT STATE OF EXPERIMENTAL RESULTS

OF DIRECT REACTIONS WITH EMPHASIS ON

NUCLEAR STRUCTURE INFORMATION

O. Hansen, J. Garrett

To cite this version:

JOURNAL DE PHYSIQUE Colloque C5., supplément au n° \\, Tome 37/ novembre 1976,, page C5-1

PRESENT STATE OF EXPERIMENTAL RESULTS OF DIRECT REACTIONS WITH EMPHASIS ON NUCLEAR STRUCTURE INFORMATION

0. Hansen and J.D. Garrett

Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark.

Résume.- Une discussion de la diffusion élastique est tout d'abord présentée et montre que les données expérimentales permettent de déterminer deux paramètres du potentiel réel: sa valeur à un point d'intersection et sa pente au rayon coulombien. Des exemples de trans-ferts d'un nucléon correspondant à de bonnes conditions de raccordements de moments angu-laires sont présentés et montrent que les conditions nécessaires à un traitement convena-ble par la DWBA sont remplies. Les données correspondant à des états voisins mais ne pré-sentant pas les conditions précédentes, ne sont pas bien décrites par la DWBA et une dis-cussion critique dans le cadre du modèle en voies couplées est présentée. Les résultats du transfert de deux nucléons sur des noyaux déformés avec de forts couplages collectifs sont montrés à titre d'exemple d'analyse CCBA satisfaisante. Les transferts de particules alpha dans la région de Pb et de Ni sont présentés et une relation simple entre transfert de par-ticule alpha et transfert de deux nucléons entre états de type paire est établie. Il est é-tabli que bien que le-mécanisme fondamental de .transfert à l'effleurement ne soit pas bien compris, il est possible d'étudier systématiquement les transferts de deux et quatre nuclé-ons pour en extraire des informatinuclé-ons sur la structure à la fois nouvelles et évidentes à interpréter.

Abstract : The talk first discusses elastic scattering and concludes that the data de-termines two parameters of the real potential, namely it's value in the point of com-mon intersection and it's slope at the Rutherford radius. Examples of well matched one nucleon transfer data are presented and it is concluded that the necessary conditions for a DWBA treatment are fulfilled . Transfer data to neighbouring states which are less well matched cannot be described by DWBA and a critical discussion of coupled channel explanations is presented. Two nucleon transfer results from deformed targets with strong collective couplings are shown as an example of successful CCBA analysis, a-transfer data in the Pb region and in the Ni region are presented and a simple con-nection for a-transfer and 2-nucleon transfer between pairing-type states is established. It is concluded that while the fundamental mechanisms for grazing, transfer are not well understood it seems possible to produce systematic data for 2 and 4 nucleon transfer with obvious and new nuclear structure information.

1. Introduction.

Transfer reactions with light heavy ions origi-nally were studied [_ 1 —3J because of curiosity. Would such reactions be similar to light ion reac-tions, or perhaps even simpler exhibiting largely semiclassical aspects? After several years, howevei the emphasis in such studies still remains on the reaction mechanism and preciously little spectros-copic information has been obtained (see e.g. ref. |_4j and the references quoted therein). The light ion induced direct reactions certainly have remai-ned the major tool for studying nuclear structure. Why then should we continue to study the mechanism of heavy ion transfer reactions, if our hopes of converting them into nuclear structure probes are small? The answer to this question, we believe, is that except for elastic scattering, grazing colli-sions with particle, or just energy and angular momentum, transfer is the mildest, least violent

process that can take place in an encounter bet-ween heavy ions. Thus one might believe that such processes should be characterized by a relatively simple mechanism which must be understood before we can reasonably claim to understand the more

vio-lent fusion or deeply inelastic events. This, of course, is a working hypothesis and it may turn out to -be wrong. However, we still think that it is a reasonable hypothesis, and in the hope that the understanding of grazing collisions eventually may provide a key to the understanding of the more violent phenomena, we shall proceed to review the subject.

The plan of the present review is to focus on certain, selected cases that are of a nature which

a -priori one would think to be simple and which the experimental data demonstrate that we do not un-derstand. Thus we will once again emphasize

C5-2 0 . IWISEN AND J .D. GAI1RETT

tion mechanism over spectroscopy, and we think ri-

ghtly so. Heavy ion grazing collisions are by and large not for spectroscopy ; they should be con- sidered as doorways for the characteristic heavy ion processes : fusion and deeply inelastic events. 2. The elastic scattering problem.

One step direct reactions are commonly described

in the DWBA as perturbations on the elastic scat- tering amplitudes. The elastic scattering wave

functions are generated by optical potentials which are vzried until the predicted cross sections re- produce the measured elastic scattering. The pre-

dicted elastic scattering is sensitive to the poten- tials only in a narrow range of distances near the nuclear surface region. Therefore, it may be asked

if the optical potential determined from fitting elastic scattering also is correct for- the descrip-

tion of the transfer reactions. For example, the transfer reactions might be sensitive to a radial

region of the potential different from that im- portant for elastic scattering (see e.g. ref. [5] ) .

Fig. 1. Plot of the real nuclear potential as a function of the separation distance for a series of potentials obtained from a fit of 100 MeV 3 2 ~ elastically scattered from 2 7 ~ 1 . The Woods-Saxon potentials, labelledby their real well depth and diffusivity (V/a), are given in ref. [6]

,

Figure 1 demonstrates a typical situation :

the collision [6] of 100 MeV 3 2 ~ ions with 27~1. All

the real potentials which fit elastic scattering

intersect at approximately the same relative dis- tance. Thus one apparently has fixed the real po-

tential at essentially one point and has learned very little about the slope of the potential. Slo-

pes (or rather Woods-Saxon diff usivities) from a S 0.45 to a 3 0.80 give essentially equally good fits to the measured elastic data, as long as the

potential goes through the common point of inter- section.

What is the physical significance of the distan- ce at which these real potentials have a common va-

lue? The elastic scattering is largely determined

by the "rainbow" part of the deflection function ;

therefore one would perhaps connect this intersec- tion distance to the apsidal distance for the rain-

bow orbit. Noting that the attractive nuclear part of the real potential at the common intersection

distance is only a small percent of the Coulomb potential, Christensen and Winther [7] treat the nuclear part as a perturbation. They find in first order that the intersection distance, rint, is gi-

ven by

r _int = rR

-

a12

-

0.65A ;

rR is the Coulomb apsidal distance for the rainbow trajectory, a is the diffusivity (or in their po- tential, the decay rate of the exponential poten-

tial), and A is the nuclear correction to the Cou-

lomb apsidal distance, roa,

with

and

2

a = Z1Z2 e

/

(2 EcSm.) is half the. distance of clo-

1 2

sest approach, and ro=(l+pr /ao2)r is the eccentri- city of the orbit given in terms of the impact Pa- rameter of the rainbow trajectory, or. The real nuclear potential is denoted Unucl.

For a given colliding system the energy depen- dence of the intersection distance is clear from

eq. (1): as the energy increases the rainbow angle decreases (moves forward) and rint becomes larger.

At sufficiently large energies, the rainbow angle

EXPERIMENTAL RESULTS I I I

-

t

opt. mod.

-

-

0 1hPt.

-

-

I '

t i

-

-

-

- r O - O -

-

-

I

-

-

I I I

E,,,

(

MeV

1

Fig.2 The solid points show the energy depen- dence of the nuclear separation distance at which the real nuclear potentials derived from 160+208pb elastic scattering intersect. The open circles show the strong interaction radius determined from the quarter point of the elastic data. For details of the analysis see ref. [8]

.

constant value of rint. The only data found perti- nent to this prediction, for the 160 + ?'08pb sys- tem, [8] is shown in fig. 2. For incident energies just above the Coulomb barrier, where the rainbow angle is moving rapidly with energy, rint increa- ses as a function of bombarding energy whereas the strong absorption interaction radius remains nearly constant. Data at still higher energies [9] are consistent with rint becoming constant.

Christensen and Winther [7] in a global analysis of elastic scattering data find a simple empirical relationship for the radius where the slope of the nuclear and Coulomb potentials are equal but with opposite signs :

'I3

'I3)

+ 2.72 fm.

r B = 1.07 (A1 + A 2 (5

This is illustrated in the upper half of fig. 3. Since we are essentially outside the nuclei at rg, it can be assumed that the Coulomb potential is known :

Therefore, it is concluded that the data fix the real nuclear potential at one distance (rint) and

Exp. pot. w ~ t h a ~0.63frn

,.

Fig.3 The radius where the slopesof the real nuclear and Coulomb potentials are equal is shown

(top) as a function of ~ 1 / 3 + ~ 2 1 1 3 for Saxon-Woods potentials which reproduce the elastic scattering in a variety of cases. Also shown (bottom) is a

similar plot for the equivalent exponential poten- tials (eq.7). Good a eemen is obtained with the dependence of rBon AFJ3+ 1 AiJ3 given in eq.5 and shown as the solid lines in this figure. The SYS-

terns used for this comparison are given in ref.7.

its slope at another (rB)

So if we assume a two parameter functional form for the nuclear potential, the potential should be well determined in this range of relative dis- tance. The authors of ref. [7] advocate a poten- tial of the proximity type

[lo]

with parameters det'ermined from their global data search :

with R = 1.233 A

'I3

-

0.978 A - " ~ fm and a = 0.63 fm.

C5-4 0. HANSEN AND J.D. GARRETT

tial to generate elastic scattering wave functions

for the direct reaction analysis.

(At this point the authors must confess that they have not been able to complete this program

for the present report. Consequently we have no new information to report at this time on the ab-

sorption part of the nuclear potential).

L 9 S ~

(gs,7/2-)

E

=56

MeV

r=,+,

,,,,

3. The one-nucleon transfer problem.

Let us first consider the simplest transfer re- action,one nucleon transfer from a doubly closed shell target to a single particle state. As an

16 15N)49sc example consider the reaction 4 8 ~ a ( 0,

which has been studied at Argonne [2,11], Pittsburgh

[12] and Copenhagen [13]

.

"Sc (

3.08,3/2')

E

=

56 MeV

L = 1 + 2

Pot FVI

Fi

.

4. Angular distributions corresponding to 48~a(16~,15~) transitions. to 49S.c (g. s.) and 29Sc* (3.08) obtained [13] at an incident energy of 56 MeV. The curves are full recoil DWBA predictions multiplied by spectroscopic factors of 2.0 for 160 + 15N and of 1.0 and 0.6 for 4 8 ~ a -+ 49Sc ground and 3.08 MeV states respectively.

~ i 4, shows the ~ . c ~ ~ 12,131 data ~ ~ment between the data and DWBA is again impressive ~ ~ ~ ~ ~ - A ~ ~ ~ ~ ~ ~

r'or the transition to the 4 9 ~ c ground state. The with regards to both angular shape and absolute angular distribution is bell shaped near the grazing magnitude. For both these examples there is good angle with oscillations superimposed. At the forward

Q and

L matching at the nuclear surface, and both angles the oscillations dominate. The full drawn cases are dominated by the normal (parity conser-

curve is a DWBA calculation made using the full- ving) L = 4 transfer with a < 10% contribution recoil, finite-range code LOLA [14] and optical pa- from the non- normal L = 3 transfer. (This state- rameters which fit elastic scattering [13]. The a- ment is based entirely on the DWBA calculations ;

greement between theory and experiment for both the nothing in the data definitively distinguishes angular shape and the absolute cross section magni- between the normal and non-normal contributions). tude is impressive. The DWBA prediction assumes

spectroscopic factors of 1.0 for the 4 8 ~ a + 4 9 ~ c (f ) transition and 2.0 for the 160 -t 1 5 ~ (plj2)

7/2

transition and no further normalization. The 40~a(13~,

12c)

41~a(g.s.) data of Bond et a1.[15] at three bombarding energies is shown in fig. 5 in comparison with recoil, finite range DWBA calcula- tions (perturbative method of ref. [16] )

.

The agree-

Returning to the 48~a(16~, 15N) reaction, let us examine the transition to the 3.08 MeV P3/2 state of 4 9 ~ c which has a spectroscopic factor of 2 0.6,

EXPERIMENTAL RESULTS

MeV

'?

6 8 M e V

Fig. 5. Angular distributions corresponding to 40Ca(13~, 1 2 ~ ) 4 l ~ a ( ~ . s .) transitions obtained [15] at 40,60 and 68 MeV incident energies. The curves are recoil DWBA calculations [16]

.

transitiontoLOLApredictionscalculatedinthe same manner as for the ground state transition and with an absolute normalization corresponding to a

4 8 ~ a -+ 4 9 ~ c (2 P?,~) spectroscopic factor of 0.9. The DWBA calculation under-predicts the cross sec- tion magnitude by 50% and it fails to reproduce the forward angle behaviour of the cross section (when normalized to the grazing peak as shown in

the figure). These discrepancies can be reduced by varying the optical parameters (see e.g. ref. [ll]) ;

however, then the problem is shifted to fitting the ground state transition. The DWBA fails to correctly

describe both the f7,2 and P3/2 transitions within

the same recipe.

The DWBA is a perturbative treatment.

A

necessary condition for its application is that the partial

wave cross section for the specific channel under investigation be small compared to the partial wa- ve cross section of both the elastic and the total

reaction cross sections for the same partial wave. The first condition is made explicitly in the DWBA

(see e.g. ref. [17] ) . The second is the result of the treatment of all the reaction channels apart fromthe one under consideration as an absorption

of flux via an imaginary pot~ntial. If the channel under consideration dominates the reaction channels it cannot be treated using the absorpti~e poten- tial obtained from elastic scattering.

The various partial wave cross sections under consideration for the 160 + 4 8 ~ a system are shown as a function of the incoming partial wave number in fig. 6. The total reaction cross section~follows

the unitarity limit for the partial waves below grazing and then falls to zero in the region of the grazing partial waves. The elastic partial wave

cross sections, which were determined from the sa- me optical model elastic amplitudes, nL,used to de-

termine the total reaction cross section, show the complimentary behaviour

.

The ( 60, 5 ~ ) partial wave transfer cross sections peak at the grazing L and

are .of the order of 3% of the total reaction and the elastic cross sections for these partial waves. Thus the necessary conditions for a DWBA treatment

are fulfilled.

Whether the sufficient conditions also are ful- filled is a much more complicated question. Follo- wing Henning et al. [18]

,

we may sum the direct partial wave cross sections over all active exit channels. (In our language an exit channel is cha-

racterized by the quantum numbers of .the nuclear states in the exit channel, i.e. ( 2 , N, Ex, ,'J

etc, for each product.) They find that for the

160 + 4 8 ~ a system at 56 MeV incident energy that about 50% of the total reaction cross section for the grazing partial wave is due to direct reactions. Such transitions can "remenlber" how they were ini- tiated and are radically different from equilibrated

compound nucleus formation. If the total Hamiltonian for the colliding system contains parts that couple such direct channels,important modifications in the flux distribution for these channels may take place.

These modifications are not included in the DWBA

treatment. Whether such couplings exist is essen-

0. HANSEN AND J.D. GARRETT

-

56

MeV

Fig. 6. Fifty-six MeV 160 + 4 8 ~ a elastic, total reaction and 48~a(160, 1 5 ~ ) transfer partial cross sections as a function of the angular momentum in the 160 + 4 8 ~ a channel. The same spectroscopic factors multiplying the DWBA predictions in fig. 4 also are in- cluded in the transfer partial cross sections shown. Note that the transfer partial cross sections have been multiplied by a factor of 10, so that they can be shown on the same plot with the elastic and total reaction partial cross sections.

emphasize that coupled situations can exist even measured

I3c

and 1 4 ~ elastic scattering be repro- if the direct cross section is only a small frac- duced)

.

Following the discussion of ref. [20] we tion of the total reaction cross section. The cru- write the L = 1 DWBA cross sections as

cia1 point is whether a coupling mechanism exists

(d~/dw)~=l=~

I

E @%IM 'yRM (8 9 4 )

I

2 or not. For the 160 + 4 8 ~ a system, this question has M 2

not been addressed. We shall discuss, however, some

other systems where couplings have been considered

quantitatively. [see however the talk of LOW]

1

I

-

(IR,R+I + IR,R-I)Y

a.

+ l

l 2

+

But first let us return to the

13c

+ 40~a reac- _{R 2}

rion and examine the + 3 9 ~ (g. s. ) exit channel. The 3 9 ~ ground state has 'J = 3/2+ and the

₁

I (I~,R+~ + lR,R-I)~R-i

l 2

4 0 ~ a -+ 3 9 ~ (g.s.) spectroscopic factor is close to R 4 (see e.g. ref. [19]). The normal L transfer for

this transition is 1 and the non-normal is 2. The data [20] were obtained simultaneously with the (13c,

12c)

data of ref. [15]. However, in this ca- se the oscillations in the DWBA predictions are nearly exactly out of phase with those in the em-

pirical angular distributions (see fig. 8). This result cannot be remedied by changes in the optical

model parameters (within the restrictions that the

Here R is the partial wave inddx in the exit chan-

nel, M is the z-component of the transferred angu- lar momentum L, and L = 1. The z-axis is the inco- ming beam direction,

pQLM

is the transfer amplitude, and ykM is a spherical harmonic. is a DHBA radial integral indexed by the partlal wave indices

+

1 in the final and initial channels. Since YR and

EXPERIMENTAL RESULTS C5-7

Fig. 8. Angular distributions corresponding to the 40ca(13~, 14N)39~ (g. s.) transition obtained [20] at incident energies of 60 and 68 MeV. The curves are recoil DWBA calculations, which show the difficulties in reproducing.the phase of the oscillations observed in the experimental angular distributions.

The maximum contribution comes from R values near the grazing partial wave (to) which is determined by the period of the oscillations in the angular

distributions (AB) to be Ro 2 35 [using (R,

+

1/2)A8 = ~ r ]

.

The phase difference between the con- secutive radial integrals I

and %,R-1 is es- R ,R+1

sentially Coulombian, i.e. 5 2 .tanq1' (lli/ !Lo) where q is the Sommerfeld parameter. In the present case the 'phase difference should be 2 30-35'. Since the radial integrals are nearly in phase for the major

contribution at R 2 Ro, the last term in eq. 9 do- minates the cross section. Consequently the L=l

angular distribution should oscillate as

The DWBA calculations follow this result, but the data do not. The data indicate that M=O is dominant, not I ~ l = l . The non-normal L = 2 contribution is cal- culated to be small and cannot contribute in the

transition to the 112' excited state at 2.53 MeV in 3 9 ~ where the same problem persits. Furthermore

the L = 2 shape would not reproduce the most for- ward angle data. Thus we are compelled to seek the

explanation of this discrepancy outside of the

DWBA.

Such an explanation has been proposed by the next speaker and his collaborators [21]

.

They pro- posed that coupling to the 3- and 5- states in 40~a are important. The routes included in the calcula-

tion are shown in fig.9.

Remove

-

---

3-

o+

-

Fig. 9. Diagram showing the couplings assumed in the CCBA ca culations reported in ref.

PI]

for the 40Ca(13C, "C) 41Ca (g. s. ) and 4Oca( 3 ~ , 4N) 3 9 ~ (g.s.) transitions.

The 40~a(13~,12~) 41~a(g.s.) transition has a strong

(j = R+1/2) direct route and a weak route through the 3- state in 40~a. The 4 1 ~ a ground state can be

-1

reached by stripping into the f712 d3/2 component of the 3- state; however, this route is dynamically weakened for two reasons : a) the transfer from the 3- state is further from the optimum Q-value than

is the direct route ; b) the dgI2 transfer from the 3- state has j = R-112, and therefore, it is weak- ened relative to the ground state j = 9.+1/2 trans-

fer.

C5-8 0 . HANSEN AND J.D. GARRETT

optimum Q-value than is the direct transition, and -1

b) the transfer from the fTIZ djI2 component of

the 3- state proceeds as pickup of the f71g parti- cle with j = %+I12 which is enhanced over the di- rect d pickup.

312

Consequently, this coupling will affect the p i c k

up but not the stripping. The CCBA calculatibns in-

dicate that the indirect pick-up route is M = 0 do- minated; hence a mechanism has been found which has

the correct properties to reproduce the data. Quan- titative agreement is obtained only by enhancing

the B3 and 65 values in the CCBA calculations con- siderably over the empirical values. Still the fit

to the experimental angular distribution is not

convincing.

This situation really is not very satisfactory.

The proposed indirect route undoubtedly contribu- . .

tes, but since the 3- state in 4 0 ~ a is not very collective (110 single particle units) other rou- tes also must be considered. In the ( 1 3 ~ , 1 2 ~ ) strip-

ping reaction,for example, dgI2 and sl12stripping from the other components in the wave function of the 4 0 ~ a 3- state also must contribute. The spec- troscop'ic amplitudes for such components are not neg-

ligible [19]. Such transitions also are dynamically enhanced (i.e. j = 11+1/2). Exit channel coupling

(e.g. 40~a(g.s.) -+ 41~a(3/~- jg4'ca (g.~.)), as well as projectile and ejectile coupling, should be

\

considered. In fact Sinclair et al. [22] explains

a parallel L = 1 26~g(13~, 12~)27~g(g. s . ) discrepan- cy by only considering projectile-ejecfile X=2 cou-

plings. Since there is no single strongly collecti- ve channel (surface vibration, enhanced two-nucleon

transfer, etc.) which dominates the coupling, one probably has to consider several channels explici- tly in order to obtain a quantitative understanding

of such cases. The number of channels which must be considered are more than the present computer tech- niques allow but are still too few to produce ave-

rage couplings that could be handled via an absorpti- ve ~otential. Conversely, this may exactly be where the interesting heavy ion physics lies; if such

problems can be handled, we may have found the path towards understanding collisions with much greater energy losses. Clearly the present situation does not allow for detailed nuclear spectroscopy with hea- vy ion onenucleon transfer reactions; but why should

we want to do spectroscopy in this cumbersome manner anyway? '

4. Some two nucleon transfer triumphs.

An entirely different situation prevails if we

study heavy-ion induced transfer reactions in the middle of the rare earth region. Here the deforma- tions are large and stable,and Coulomb-nuclear exci-

tations within the ground state rotational band ta-

ke place with large probabilities. For example, for Xe plus Er at incident energies near the Coulomb barrier, the predicted multiple Coulomb excitation

probability, o(excitation)/o(elastic)

,

approaches unity for the back scattered particles. Similarly the predicted excitation probability of the Er in its 10+ state is o(lo+)/rel % 0.1. Under such con- ditions there is no question of'using DWBA, since the transfers dominantly take place from excited

states. Transfer experiments as indicated have not been studied because experimental energy resolutions

< 100 keV are needed. Light heavy ion transfers, however, have been studied by Erb et al. in this mass region using

I2c

beams [23-251 and quite dramatic coupling effects have been demonstrated.

The experimental technique is quite rigid. A

12c

beam from a Van de Graaff (the MP's at Brookhaven), a thin target, a Q3D spectrometer and a focal plane detector for position information and ion-identifi-

cation. The high resolution and large solid angle of the spectrometer are essential. A spectrum from the 1 8 6 ~ ("c,

14c)

1 8 4 ~ reaction is shown in fig. I0

demonstrating an energy resolution of 5 70 keV. The

first 2' rotational state at 1 1 1 keV is clearly resolved from the ground state. The ground-state to ground-state distributions display the expected semi- classical, grazing angular distribution; however,

the 0+ + 2+ (fig. 11) and 0+ + 4+ transitions split into almost two bell shapes with a minimm in the

middle. The forward bell shape changes in intensity from the light rare earths to the heavy, where it

has almost disappeared. These effects cannot be ex- plained in the DWBA, but follow from coupled chan-

+

+

nel calculations that include the 0

,

2 and 4' ground state band rotational levels in both target and final nuclei. Without the multiple Coulomb ex- citation the interference dip in the angular distri- butions is not predicted; therefore it can be con-

cluded that these data represent cases where the transfer to a larg'e extent takes place from an ex- cited state. Besides angular distribution shapes the CCBA analysis explains relative cross sections

. .

EXPERIMENTAL RESULTS

POSITION CHANNEL

10 Particle spectrum corresponding to the

l s s $ f i c , li,) 184 W reaction at an incident energy of 7 0 MeV obtained [23] with a Q3D spectrometer. tational band. Also it is not simply an isolated case that has been investigated, but a systematic trend for a series of targets through out the ra-

re earth nuclei. This is one of the first examples of new spectroscopy with heavy ions. Although simi-

lar effects exist in the light ion rare earth (t,p) and (p, t) data [26], they are m c h more dramatic for the heavy ion induced reactions.

It must be remembered that the absolute norma-

lization of the two nucleon transfer calculations remain as an outstanding theoretical problem. In general the experimental cross section is underpre-

dicted by from a factor of 10 to over a factor of

100. We have no further comments tooffer as the pro- blem seems to be entirely open at this time.

5 . Four nucleon transfe'r reactions and a little mo- re about two nucleon transfer.

Four nucleon transfer spectroscopy is one of the obvious goals for light heavy-ion reactions. a-par- ticle correlations play a significant role in nu- clear structure, still very little solid information

exists from transfer experiments. Recalling the discussion of the one nucleon transfer reactions (sect. 3) and noting that the amplitudes for the transfer of four particles are much smaller, we should obviously not be naive about the reaction me-

t - .

I I

I I

Fig. 11. Experimental and theoretical 2fangular distributions for

14c)

transitions on several rare earth targets..The theore ical curves are CCBA calculations described in ref. 1251

.

chanism. And yet, as we shall try to show, it may not be such a bad attitude to be" deliberately naive'!

160 12

Let us first examine the (

,

C) results in the Pb region as studied at Rochester and Chalk River

[27-301. The experiments were made at tandem ener- gies, 93 MeV at Chalk River and 8 8 MeV at ~ochdster. Spectrographs with advanced on-line detectiori'sys- tems were used at both places (see e.g. ref. [31] for the Rochester set up) and energy' resolutions of

3 200 to 2 5 0 keV were obtained for reactions with typical cross sections below 1 ub/sr. Table.] sum-

0. HANSEN AND J.D. GARRETT

Table 1

Comparison of from (I60,l2c) reaction and a decay.

Transition

2

peak da/dR yo fkeV)

( ~ b / s r )

(160, 12c)-' a-decay

and Bi targets. The main 'idea is to compare the a-stripping cross sections, reduced for reaction

kinematics to a-decay data (proceeding in the op- posite direction) also corrected for kinematics

(barrier penetrabilities). It appears from the ta-

ble that the overall agreement is impressive. The Q-corrections to the reaction data are large; let us compafe e.g. the 204~b and the 208~b results.

The 208~b -+ 2 1 2 ~ o (g.s.) transition. proceeds with a cross section that is 15 times larger than that of the '04Pb + 208~o (g.s.) reaction. The a-widths derived from the transfer intensities for the two cases only differ by a factor of 3 3.6 and they are in agreement with the decay data. This gives some

160 12

confidence that the (

,

C) reaction indeed "mea- sures" a nuclear matrix element of the form

ref. [32]) so it should be a reasonable region to

look also for a-vibrations. We would describe an a-vibrational state as a special combination of

proton and neutron pairing vibrations. In 208~b

a proton pair and neutron pair should be organized in the same orbits and with the same correlations

as they appear in the ground state of 2 1 2 ~ o , simi-

larly four holes should be organized in such a 204 way that they simulate the ground state of Hg,

i.e. symbolically

The energy of the state (12) to lowest order is

B ( ~ " ~ H ~ ) = 8.44 MeV

+

(13)

< final

I

[a+(proton)a+(proton) a+ (neutron) a (neu-

tron)] "07

1

initial > (1 0) where B stands for binding energy. This state is

+

+ clearly related to the pairing coupling scheme. If

i.e. for the 0 -+ 0 transfers we may assume

there were no interactions between the proton-pairs

where the coherent sum is over the participating

shell model orbits and all2 is an intrinsic trans-

fer amplitude which depends on the fermion quantum numbers aS,well as on binding energies etc. We ha-

tre not included the L=2 transfer of an alpha parti- cle in its 2+ first excited state based on the agree. ment with the decay data, where the a-appears in

its ground state.

The Pb region exhibits some of the clearest ex-

amples ofpairing vibrational -excitations (see e.g.

and the neutron-pairs it would go exactly into the pairing vibrational scheme as a four-phonon state. However, the ground states of 204~g and 2 1 2 ~ o do

show some extra binding (% 1 MeV) in addition to what is obtained from the pairing alone. Thus the

state (12) is rightly termed a-vibration and it should satisfy

In the "harmonic" limit that we are discussing, the Q-value is the same for the two reactions involved

and therefore the relation (14) can be taken to apply to the experimental cross sections directly.

EXPERIMENTAL RESULTS

ge the excitation energy of the state (12). Broglia The 204~g(160,

12c)

reaction was studied at and Bortignon [13] calculate a change of 2 1.2 MeV Rochester [30] this spring on a 204~g target pre- down to 3 7.2 MeV of excitation, the main part of pared at University of Aarhus. The result is shown which is the Coulomb attraction between protons _{in fig. 12.}

and proton holes.

12 208 2 0 4 ~ g

(160,

C)

Pb

E

, G ~ =

88

MeV

KINEMATICALLY COMPENSATED

44

_SUM

_OF

_eL

₌

80°,85"AND 90"

Cn 36- i-

I COUNTs 21

nb/sr

z

2

28- 0 .20- 12 - 4 - a m 1- mm I m n 10 9 8 7 - 6 5 4 3 2 I ₀

EXCITATION ENERGY (MeV)

204 16 Fig. 12. Sum of kinematically compensated spectra corresponding to the Hg( 0, I2c)208pb reaction at an incident energy of 88 MeV

.

A peak corresponding to the ex- pected cross section for the transition to the a vibration state is shown by the das- hed line at the predicted excitation of 7.2 MeV.

NO sicgle state could be identified below Ex=9 MeV, _{make simple relations between Q-corrected 4 and 2}

and at Ex=7.2 MeV, the predicted energy of the a- _{nucleon transfer cross sections between such sta-} vibration,the summed background is l e s ~ than 30% of _{tes. Taking as an example the even cd-isotopes as} the expected. cross section of

a

750 nb/sr (see ta- _{targets :}

ble I). Thus these Pb data do indeed produce new

spectroscopy. ~ ~ ( ~ ' ~ c d ( ~ ~ ~ , ~ ~ ~ ) ~ ~ ~ s ~ gs ) / [ C F ~ ( ~ ~ ~ C ~ ( ~ ~ O , ' ~ C ) 112~ngs)

Let us follow the pairing-a-transfer idea a lit- _{x ,Q(l 12Sn(14C, 12C)}

_14sn,,>]

₌

6"

tle further. Disregarding for the moment the iso

-

16 12 116

spin coupling in (lo), we can rewrite the nuclear UQ(112~d( 0, C) Sngs)/[uQ(112~d(160,14~)114~ngs) matrix element as

E <fla+(n,)a+(a2)a+(vl)a+(v2)li> II W

+

+

+

The only other low lying O+ states in Sn that

=X E <f(a (nl)a+(x2)(a><ala (vl)a fv2)li> (15)

a nv should be strongly excited in a-transfer reactions

are the proton pairing vibrations, so far not known.

= E ( E <f

1

a+(sl)a+(s2)

I

a>j (~<a/a+(~~)a+(v~)] i>) _{Such experiments (first suggested to our knowledge}

a s V

by von Oertzen [4]), should prove exciting both as tests for the assumptions about the nuclear matrix For a situation where the neutrons are superfluid

elements involved and for the possible spectroscopy. the second term is large only when la> is the ground .

Other relations of the same nature as (16) can rea- state of

l

i + 2 neutrons>. Thus the strong O+ a-

dily be developed. transfers.wil1 be to states that are strongly popu-

lated in two proton transfer proceeding from

1

a>= As a last example of the interplay of 2 and 4

C5- 12 0. HANSEN AND J . D . GARRETT

ground s t a t e and 3.31 MeV O+ s t a t e s of 6 0 ~ i . From t h e 5 8 ~ e (h,n) 6 0 ~ i experiments l34,35] t h e e x c i t e d 0' s t a t e a t 3.31 MeV has been i d e n t i f i e d a s a pro- t o n p a i r i n g v i b r a t i o n a l s t a t e , i . e . t h e t r a n s f e r - r e d proton-pair moves a s i n t h e ground s t a t e o f 6 2 ~ n . The i s o s p i n and Q-value reduced e m p i r i c a l

(h,n) c r o s s s e c t i o n s s a t i s f y : oreduced 58 _{( Fe(h,n)} 60 _{Ni(3.31, 0 + ) ) 2}

0.40 reduced 60 ( ~ i ( h , n ) ~ ~ Z n ( g s ) ) (17) and t h u s t h e s t a t e h a s % 50% p a i r i n g v i b r a t i o n a l c h a r a c t e r . The same s t a t e s can be s t u d i e d i n t h e

6

a - t r a n s f e r r e a c t i o n s . 5 6 ~ e ( Li,d) r e s u l t s from Rochester [36] and Los Alamos [37] have been r e - p d r t e d w i t h good r e s o l u t i o n

.

Under t h e assumption t h a t t h e a - t r a n s f e r h e r e can be d e s c r i b e d a s two L = 0 di-nucleon t r a n s f e r s , proceeding v i a t h e in- t e r m e d i a t e ground s t a t e a s t h e s o l e r o u t e , t h e em- p i r i c a l r e l a t i o n (17) f o r (h,n) should a l s o be va- 6 l i d f o r ( L i , d ) , i . e . we expect [38] using a - t r a n s i t i o n s from t a r g e t s t h a t a r e i s o t o n e s . E q . (18) i s indeed f u l f i l l e d . S t e i n e t a l . [37] t a k e t h e i d e a f u r t h e r a n d i d e n t i f y t h e p r o t o n p a i r v i b r a t i o n i n 6 2 ~ i from t h e a - t r a n s f e r r e a c t i o n , a s t a t e n o t known b e f o r e . A s t e p f u r t h e r : a p a i r v i b r a t i o n a l s t a t e exhi- b i t s a symmetry i n r e g a r d t o p a i r - s t r i p p i n g and p a i r pick-up. I f we can r e a c h t h e p r o t o n 2 p a r t i -

+

cle-2 h o l e 3.31 MeV 0 s t a t e i n 6 0 ~ i by adding two p r o t o n s i n Zn o r b i t s and l e a v i n g t h e two proton- h o l e s of t h e Fe t a r g e t i n t a c t , we should a l s o be a b l e t o r e a c h t h e s t a t e from t h e Zn-target by pic- k i n g up from t h e protons below Z = 28, c r e a t i n g t h e F e h o l e - p a i r . No di-proton pick-up d a t a e x i s t , b u t

6

why n o t t r y w i t h a-pick up ? I n t h e (d, L i ) reac- t i o n , we should t h e n expect t h a t

w r i t i n g a g a i n t h e r e l a t i o n f o r i s o t o n e s . T h i s ex- periment was done r e c e n t l y a t Groningen [39] w i t h t h e r e s u l t t h a t t h e 3.31 MeV s t a t e i s populated 'L 5 times more weakly t h a n expected ( s e e f i g . 13). New n u c l e a r s t r u c t u r e information, which h a s n o t

EXPERIMENTAL RESULTS C5- 13 Thus it seems to us, taking a deliberately naive reactions in connection with deep inelastic scatte- view point, that 2 and 4 nucleon transfer reactions ring and other characteristic heavy ion processes have much to offer in terms of new spectroscopy. rather than viewing them separately.

In a less naive light we have to admit that the _{Acknowledgement : The authors should like to acknow-} reaction mechanism of light heavy ion induced reac- _{ledge discussions with P.R. Christensen,B.S.Nilsson} tions are puzzling and complex. _{and Aa. Winther that were helpful in preparing} Perhaps our long term view should be to see these _{this talk.}

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