ALPHA-TRANSFER REACTIONS

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ALPHA-TRANSFER REACTIONS

K. Bethge

To cite this version:

K. Bethge. ALPHA-TRANSFER REACTIONS. Journal de Physique Colloques, 1971, 32 (C6), pp.C6-

87-C6-90. �10.1051/jphyscol:1971612�. �jpa-00214830�

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ALPHA-TRANSFER REACTIONS

K. BETHGE

11. Physikalisches Institut, Universitat Heidelberg, Germany

Resume.

-

Les &tats de parite negative dans IsN et ^{1 7 0}sont etudies par des experiences de transfert de particule a. Des calculs utilisant l'approximation de Born avec ondes deformkes et portee finie ont ete faits pour dkrire les distributions angulaires des etats de parite negative dans

1 7 0 .

Abstract. - Negative parity states in 1sN and ^{1 7 0}are investigated by alpha transfer experiments. Finite range DWBA calculations have been performed to describe angular distributions leading to negative parity states in ^{1 7 0 .}

Introduction. - During the last years the a-transfer has been investigated on a large number of nuclei using different heavy ion reactions [I]. The nucIei at the beginning of the s-d shell attracted most atten- tion because the concept of many particle-many hole states for the description of the structure of a number of excited states in these nuclei was found to be well established. As a result of reactions leading to 1 6 0

and 20Ne, rotational bands have been established which are of 4p-4h type in 1 6 0 starting at the strongly deformed first excited O + state at 6.06 MeV.

In 20Ne a 4p-Oh band is built up on the ground state. As Horiuchi and Ikeda [2] pointed out, two rotational bands are expected in 20Ne due to different geometrical arrangements of five a clusters. In addition to the positive parity band mentioned above a negative parity band starting at the 1 - state at 5.80 MeV has been found. Both bands are almost selectively excited in a-transfer reactions.

Furthermore similar band structures have been found in neighbouring nuclei e. g. I9F. Taking the weak coupling scheme [3] into account, these band structures can be explained as the coupling of a negative parity hole to the rotational states in 'ONe [4].

The present report is concerned with results on nuclei neighbouring 1 6 0 . If a particle is coupled to the 4p-4h band a systematic scheme of negative parity states of 4p-3h type is expected in 170, if a hole is coupled to the same band a 4p-5h band should be present in 15N.

Investigations on 170.

-

The 170 nucleus has been investigated by the a-transfer reactions 13C('Li, t) and ' 3 ~ ( 6 ~ i , d) [5, 61. Almost all of the known states below 10 MeV excitation have been excited but a more preferential excitation of negative parity states has been found. Shell model calculations [7], [8]

have shown that the wave functions of the negative

parity states are mainly composed of 4p-3h and 2 p-l h components. Some of these states may therefore correspond to the 4 p-4 h rotational band coupled to one additional p,,, nucleon. These states are shown in figure 1. This correspondence has been

"N negotive MeV parity

t

positive parity

I

170 negotive

parity

/Op-*

^" ^;¹ ^-^_

--:>\A

^Op-Oh ⁰^.

_I-..-

FIG. 1. - Comparison of negative parity states of IsN and

1 7 0 with the 4p-4h rotational band of ^160.

shown by a comparison of angular distributions [5].

Excellent agreement has been found for the 0'-112- and 2'-312-, 512- states. The question remained whether this picture can be extended to the 4+-712-, 912- states also. It was known for some time [9]

that a state at 8.9 MeV in ¹⁷⁰with spin 712- has a measured a-width of T , / r

-

1.0. This state was assu- med as one component of the doublet. In the 13C(7Li, t) reaction a state at 8.46 MeV had been excited extre- mely strongly [5] but the spin assignment was ambi- guous so that a definite conclusion could not be drawn.

Therefore in addition the five particle transfer

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971612

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C6-88 K . BETHGE

reaction

12c

(7Li, d)170 has been measured [6]. This reaction exhibits an alnlost pure compound nucleus behaviour. All the measured angular distributions show a symmetry about 90°. These angular distributions could very well be described by a Hauser- Feshbach calculation. The Hauser-Feshbach diffe- rential cross section contains the transmission coefficients for the entrance and exit channels of the compound nucleus reaction. Via the transmission coeffi- cient of the exit channel this cross section is dependent on the spin j' of the residual nucleus.

In particular the angle integrated cross section is proportional to 2 j'

+

1. This dependence is no longer linear with increasing j' as shown by McDo- nald [lo].

The transmission coefficients have been obtained from optical model analyses of elastic scattering data.

The spin values determined by that method agree very well with the already known spins. This method has the additional advantage that spin combinations for unresolved states can be estimated. In the 1 7 0

spectra we found an unresolved group of three states around 8.5 MeV. By applying the above mentioned method we found that these three states must have one of the following spin combinations : 912, 712, 512 ; 912, 712, 312 or 912, 512, 512. In all combinations a spin of 912 occurs. Since our spectrum of the 13C('Li, t ) I 7 0 showed a very strong peak at 8.46 MeV we assigned a spin of 912 to that state and dare the hypothesis that this state is the second member of the doublet corresponding to the 4p-4h 4' state in 1 6 0 at 10.36 MeV. We therefore know the negative parity states in 170 which correspond to first three 4p-4h states in 160 (Fig. 1).

Investigations on 15N. - The neighbour to 1 6 0

on the lower mass side is 15N which has one proton hole in the p,,, shell. This nucleus can be formed in a four particle transfer reaction by transferring the

@-particle to B. The

' '

B nucleus has, however. a hole in the p3I2 shell, therefore only states with configu-

rations including a hole in the p,,, shell sho~tld be populated.

If the four transferred nucleons fill the empty p,,, shell in 15N a Op-lh state is formed with spin 312-. This state was identified as the low lying 3/2- state at 6.32 MeV.

In a four particle transfer reaction as e. g. 11B('60, l2C)l5N this state is excited [ I l l with only medium strength.

If the four particles are captured in s-d states, a 4p-5h rotational band similar to the 4p-4h band in 1 6 0 must be expected. This band starts again with a single 312- level and continues with level quadruplets due to the coupling of spin 312 to integer angular momenta 2, 4, 6, etc.

Because of the large number of holes this band is expected to appear at high excitation energies. In the 11B(7Li, t)l5N reaction performed at low energies [I21 a 312- state at 9.15 MeV is strongly excited.

This state has been proposed to be the band head of the 4p-5h band.

In order to get more information about the orde- ring of levels, transfer reactions leading to "N have been performed in which different numbers of nucleons are transferred 11 I]. The results clearly indicate that in the different reactions different states are strongly excited.

Therefore one may assume that the four particle transfer should mainly populate states of the expected 4p-5h type. Unfortunately in the "B(160, 12C)15N reaction the members of the quadruplets have not been clearly resolved and identified. However two groups can be distinguished : one is centered around 10.5 MeV, the other one above 13 MeV. Asindicated in figure 1 the first one mentioned may be the quadruplet corresponding to the 2' state at 6.92 MeV, the second one to the 4+ state at 10.36 MeV in '%.

Since light reaction products like tritons are better to analyse than 12C the reaction "B(?L~, t)ISN has been investigated at 24 MeV. A spectrum is shown in figure 2 [13].

--... .

I

400- I

15 23

I

1 ,,,

¹⁰¹

i I I ~ B ( ' L o , ~ )"N

I 2 4 MeV

MO-

I 5.

i

' I _.

_, .:

P I :

,

,:>' $4 +,. . >-, .L-,dL-,d-

.

I M O 13M K W Y M IYX) I S M 643 I&

FIG. 2. - Trition spectrum of the I IB(7Li, t ) l fiN reaction at 24 MeV.

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The 312- state at 9.15 MeV is very weakly excited because it implies a A1 = 0 transfer which is less favoured in (7Li, t) reactions. Strong states appear at 10.8

+

0.1, 13.028, 15.29 and at about 17 MeV.

The state at 10.8 MeV has spin 312- [14] and can belong to the A1 = 2 quadruplet. The 13.028 MeV state has a preliminary spin assignment of 1112- [14]

and may be a member of the 1 = 4 quadruplet. The spins of the later two states are not determined so far. Most of the strongly excited peaks are composed of several states which are partly or poorly resolved.

The analysis of this reaction has not yet been com- pleted. In particular nothing is known on the split- ting of the quadruplet components. The band heads of the 4p-5h and 4p-3h bands differ each by 3 MeV from the 4p-4h band head.

Dynamical effects.

-

The structure of the final states is not the only quantity which is of importance in the investigation of four particle transfer reactions.

A large cross section can also be obtained in a dyna- mically favoured case. For instance the angular momentum balance in the ( 6 ~ i , d) and (7Li, t) reactions plays an important role [15]. Since the Q-value of both reactions is almost the same the difference of the behaviour of the two reactions is due to the ini- tial relative momentum of the ^crparticles in the pro- jectiles and the associated recoil effects.

The only source of angular momentum transferred in a (6Li, d) reaction is the change of ki to kf in the process. Thus the two vectors have to be tilted against each other except for A1 = 0 transfers. In the (7Li, t) reaction one additional unit of angular momentum is already available and larger angular momentum transfer can already be achieved at smaller angles, particularly at 00, which was also found experimen- tally. The A1 = 0 transfer should however be less favoured. This implies that even at low energies (20 MeV) low angular momentum transfer takes place with reasonably strong cross sections. Thus in a complete description of four particle reactions structure and dynamical effects must be considered.

DWBA-Analysis. ^-Several attempts have been made to describe the reactions in terms of the usual DWBA methods. It was obvious for some time that any reduction of the six dimensional integral by simplifying assumptions yielded results with limited success. Recently two codes have become known which take the finite range into account [16], [17].

Both have been applied to lithium induced reactions.

In figures 3-5 experimental results for thet3 C(7Li, t)170 reactions at 17 and 20.5 MeV are presented.

The solid curvcs represent calculations which include 4p-3h and 2p-lh amplitudes in the bound state wave functions taken from Zuker et al. [7].

In computing the cross sections the interference terms are included. Furthermore for the 512- and 312-

5 ,

E l a b = 18 MeV ( _ I

i

FIG. 3.

-

Angular distributions leading to the 112- state in 170.

The solid curve is a FRDWB calculation including 4p-3h and 2p-lh amplitudes. The dashed curve includes the 4p-3h

amplitudes only. Ordinate in mb/sr.

state the three contributing L values (1, 2, 3) are added incoherently. The structureless shape of the (7Li, t) angular distributions which is due to the addition of 3 contributing I-values, is therefore very well reproduced.

The angular distribution for the 112- state shows a constructive interference between the terms whereas those for the 512- state show a destructive interference which shifts the cross section calculated only with the 4p-4h component higher up.

In general the agreement is quite good : in particular the order of magnitude comes out correctly.

The agreement in fitting the fine structure of the shape of the angular distributions is less good, particularly in the (6Li, d) reaction. The calculations have been performed using optical model data, obtained from the first elastic scattering experiments of 6,7Li [Is], Recently several new sets of parameters became available which may improve the fits to the shape of the angular distributions. The bound state wave functions of the ¹⁷⁰states only include the p,,,, s,,, and d,,, configurations. Therefore the agreement of the experimental data with the calculations is good for the transfer to the 112- and 512- states but about an

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C6-90 K. BETHGE

E, (170) = 3.85 MeV ( 5 / f )

FIG. 4. - Angular distributiotls leading to the 512- state of

1 7 0 solid and dashed curve see legend figure 3.

order of magnitude difference occurs for the 3!2- state which could be an indication that the d3!, component is missing in the wave functions and it would be interesting to repeat the calculations with these components included. The results show that a proper finite range DWBA is able to describe also many-particle transfer reactions. As Kubo and Hirata pointed out, this method can always be applied if a reaction can be considered as a cluster stripping process with loosely bound clusters. This, however, is the case in lithium induced a transfer reactions.

Frci. 5. - Angular distributions leading to the 312- state of ' 7 0 .

Solid and dashed curve see legend figure 3.

Acknowledgement.

-

Most of the experiments reported in this report have been done in cooperation with Horst Schmidt-Bocking and Walter Kohler.

Many clarifying discussions with W. v. Oertzen and H. Yoshida are greatly appreciated.

References [I] BETHGE (K.), Ann. Rev. Nucl. Science, 1970, 20, 255.

[2] HORIUCHI (H.) and IKEDA (K.), Progr. Theor. Phys., 1968, 40, 277.

[3] ARIMA (A.), HORIUCHI (H.) and SEBE (T.), Ph-VS.

Letters, 1967, 24B, 129.

[4] MIDDLETON (R.), Proc. Fifth Conf. Nucl. Reactions Induced by Heavy Ions (ed. R. Bock, W. Hering, North Holland, 1970), p. 277.

[5] BETHGE (K.), PULLEN (D. J.) and MIDDLETON (R.), Phys. Rev., 1970, C 2, 395.

[6] SCHMIDT-BOCKING (H.), BROMMUNDT (G.) and BETH-

GE (K.), Zeitschr. f. P/zy.sik, 1971, 246, 43 1.

171 ZUKER (A. P.), BUCK (B.) and Mc GRORY (J. B.), BNL-report 14085, 1969.

[8] BOBKER (J.), Phys. Rev., 1969, 185, 1294; 1970, C 2,322.

[9] BARNES (B. K.), BELOTE (T. A.) and RISSEK (J. R.), Phys. Rev., 1965, 140, B616.

[lo] MAC DONALD (N.), N L I C ~ . Phys., 1962, 33, 110.

[1 1] SCHLOTTAUER-VOOS (U. C.), Thesis Heidelberg, 1970.

[12] Mc GRATH (R. L.), Phys. Rev., 1966, 145, 802.

[13] KOHLER (W.), SCHMIDT-BOCKING (H.) and BETHGE (K.) (to be published).

[14] AJZENRERG-SELOVE (F.), NIICI. Phys., 1970, A 152,l.

[IS] OERTZEN (W. v.), Joensun Summer School Lectures, 1971.

[16] KUBO (K.) and HIRATA (M.), INS-report 166, 1971.

[17] YOSHIDA (H.), private colnmunication.

[18] BETHGE (K.), FOU (C. M.) and ZURMUHLE (R. W.), Nucl. Phys., 1969, A 123, 521.