Investigation of 15N by the reactions 11B(7Li, t)15N and 10B(7Li, d)15N

1.E.I: 2.G[

Nuclear Physics A262 (1976) 1 1 3 - - 1 2 4 ; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

I N V E S T I G A T I O N OF lSN

BY T H E R E A C T I O N S 'IBt~Li, t)'SN AND '°B(~Li, d ) ' ~ W. KOHLERt, H. SCHMIDT-BOCKINGtt and K. BETHGE~t IL Physikaltsches Instttut, Universitdt Heidelbero

Received 5 February 1976 Abstract: The 'aN nucleus was investigated by two reactions at 24 MeV bombarding energy. The angular distributions were analysed by direct reaction and compound nucleus reaction model. The level structure of ~aN up to 17 MeV could be explained in the presently known framework. In particular, the strong excitation of the state at 10.7 MeV leads to an additional spin determination of | which indicates the existence of a second state at that energy. This high-spin state probably has mainly a 3p-4h configuration. E

[

NUCLEAR REACTIONS 11B(~Li,t), IoB(TLi, d), E = 24 MeV; measured ~7(0).

I

1 aN deduced levels, J. Enriched target, F R D W B A analysis.

1. Introduction The excitation spectra of nuclei in the neighbourhood of doubly closed shells show features similar to those of nuclei on the doubly closed shells. The nucleus 15N, having one proton hole in its ground state, is a good subject for investigations when compared to xSO, because the many-particle many-hole excitations are expected to be similar for both nuclei, regardless of the different ground-state configurations 1). The two reactions chosen for the complementary investigation have previously also been used for studying 1~O [ref. 2)] because the different reaction mechanisms enhance different features of excited states. The reaction (~Li, t) selectively populates states of suitable configuration whereas the five-particle transfer preferentially populates high spin states. In addition, the triton transfer reaction 12C(7Li, ~)~SN [ref. a)] having shown a striking selectivity in populating states in 15N can serve as a further valuable source of complementary information on the level structure of the residual nucleus. A large number of other investigations are known 4 - ~ ) which can be used to complete the picture of this nucleus considerably. The structure of levels above 10 MeV, where particle-hole states dominate, is of particular interest.

2. Experimental arrangement and results The reactions were studied using the Li beam of the E N tandem accelerator of the Max-Planck-Institut ffir Kernphysik at Heidelberg s). The reaction products were * Present address: Interatom, Bensberg bei K61n. ** Permanent address: Institut ~ r Kernphysik, Universitat Frankfurt am Main, Frankfurt/Germany. 113

114

W. KOHLER et al.

detected in a scattering chamber with a vertical reaction plane 9), whereby the resolution could be improved, since the geometrical beam position at the target normally varies in the deflection plane of the analysing magnet. The particles were detected with solid state detectors and the resulting signals analysed on-line with conventional pulse handling equipment. An overall resolution of about 90 keV for the triton spectra and 75 keV for the deuteron spectra was obtained. Up to seven detectors at different angles were used simultaneously. Thus the ejectiles p, d, t, ~, 6He, 6Li, 7Li, 9Be were detected simultaneously 1o). The preparation of the boron targets is described elsewhere 1~). They were produced from 96 ~o isotopic.ally enriched material, with a thickness of about 50 #g[em 2. A contamination by 12C and 160, of about 10 % and 12 %, respectively, was determined. Typical spectra of the two reactions are shown in figs. 1 and 2. Angular distributions for the states predominantly excited in the two reactions are shown up to 15.37 MeV in figs. 3, 5, 6. The figures also contain the results of calculations assuming direct and compound nucleus reaction mechanisms, respectively. All the deuteron angular distributions show little structure except for an obvious symmetry about 90 ° . For states below 8 MeV excitation energy the angular distribution could not be measured at small angles because of the high kinetic energy of the ejectiles. The statistical errors of the cross sections measured are small enough for a restriction of the calculations to only one value of the spin of the final state. The maximum differential cross sections and the integrated cross sections for the states under discussion are given in table 2. It can be seen from a first inspection that in both reactions almost the same states are strongly excited.

3. Analysis o f the data 3.1. FRDWBA ANALYSIS

The four-particle transfer reaction showing the features common to all direct nuclear reactions, led to the application of a FRDWBA program 12) for the analysis of the angular distributions. The differential cross sections for a transfer reaction A(a, b)B with a = b + x and B = A + x can be written as follows t2): do

_/:,/~b _

dl~

(27rh2) 2

kb 2 J e + l

~

[ ~ i,(21+I)½S~S~W(LIj ' L2J2; SxI)~LIN2L'(O)I2, N2L2

(1) where J^, Jn and s x are the spins of the target, residual nucleus and particle transferred, respectively, and $1 and $2 the spectroscopic factors for the transferred particle in the residual nucleus and in the projectile, respectively. Further, RNtL,S~L2fA~ ~,l,, ~v/ is the finite range amplitude. The angular momentum transferred, L is given by ! = LI-L2 = I1-I5,

(2)

o

z

Q~ • .--~

-J

•

Z

-ii -§

0

z ,-1 ~Q

.§

:

f..,

°

~

I

!

t O

Z

z

X

O u h O

100

200

300

400

4

6

e

12

14

16

'~/~J/,.

17.1|

18

20

~/~l,

Fig. 2. Deuteron spectrum from the ;°B(TLi, d)~SN reaction at 30°.

10

A

~

22

3 0k~ev

Et,e~te~

24

,o,,,1o.,i

I°B (~Li.d )15N

m

O

15N

117

where L t, L 2, J t and J2 are the orbital and total angular momenta, respectively, of the transferred x-cluster in the residual nucleus and projectile (subscripts 1 and 2, respectively). The weight of the contributions from different/-values is given by the Racah coefficients W(LtJtLzJ2: s,l) which involve an inherent dependence on the value of Jr- The angular distributions obtained are shown in fig. 3. For the state at 9.152 MeV, the contributions from L t = 0 and L t = 2 are shown separately, whereas for the other states only the sum is given. Even though the angular momentum L t of the captured cluster is unique, in general three different /-values, namely l = LI, L t + l, contribute to the differential cross sections. Since the program could not handle values o f I > 6, only one value of I is used for the calculation of the differential cross section for the state at 15.37 MeV. The analysis was performed for the states most strongly excited. TAmE 1 Optical model parameters V

rot

a,

W

rol

(M©V)

(fro)

(fm)

(MeV)

(fm)

at (fro)

7Li-~IB 7Li-IOB t-tSN

63.9 152.0 153

1.88 1.28

0.59 0.77

9.3 (D) 7.9 (V)

86.7

0.54 0.81

17.4 (D) 14.4

0.95 0.86 0.55

d-tSN

1.42 1.74

1.64 2.36 1.56 2.03

0.68

Ref. this analysis ts) 13) t,t)

V is volume absorption and D is surface absorption. The optical model parameters for ~Li on t t B were obtained from a fit to the elastic scattering. The parameters for 7Li on t°B and for the exit channels were taken from refs. 13, 1,). The parameter sets are given in table I. 3.2. COMPOUND NUCLEUS ANALYSIS In general the t OB(TLi' d)tSN reaction shows symmetrical angular distributions, which should allow analyses of the reaction in terms of a compound nucleus reaction. This assumption is further supported by features exhibited in fig. 4. The excitation energy is plotted against the angular momentum in the entrance and exit channels. Those states which fall within the parabola are expected to be excited in the reaction, preferentially those with high spins. From fig. 4 it can be inferred that spins up to ~z~ h should occur. The angular distributions measured were compared with a calculation of the absolute differential cross sections according to (dd_~/

= (21A+ 1)(2I.+22 1) Z| ZRL

T~2z(l o) ~T~I ×

i;

L) r), (3)

~0 ~

"ID1 :J

'

19

37

?s

9

.

.

~

t

E= : 13.028I q e V ~ ~

Ex = 10.70MeV

Ex :

lSS

93

1,2

~.

~Ex = 13.84MeV

angle [c.m.]

s6

E= = 15.37MeV

~ ~

1

1B ( 7Li, t )

13,

~1,

I

9.829, 10.70, 13.028, 13.84, 15.37 MeV in the (?Li, t) reaction.

:ig. 3. Triton angulardistributions for the population of statesat 9.152,

)

10 -10:

"o 10~. ~

10

LI:2

I ~ .

lO'

0

5

10

15

2'0 I (1~)

108(?Li,d ) 15N ELAe=24 MeV

:ig. 4. Excitation energy versus angular momentum of ingoing and outgoing reaction channels.

2

'-----

=.q

J0

119

ISN

which describes the excitation of a single level at energy EB with spin IB in the reaction A(a, b)B [ref. 16)]. Here the relation S1+11

=

I

=

$2+i2

(4)

holds with channel spin S = l+i. The indices 1, 2 indicate the entrance and exit channels, respectively. The summation over orbital angular momenta 11,/2 and the spin ! of the compound nucleus takes care of angular momentum and parity conservation. The coefficients Z contain ClebschGordan and Racah coefficients, XI is the wavelength of the incoming particle a, the T~ are the transmission coefficients and PL the Legendre polynomials for partial waves I. The total decay width g(I) of the compound nucleus contains a s-mrnation over discrete levels of all open reaction channels b' and B' up to the excitation energy Ec and an integration over the level densities p(E, I) [ref. 17)] in the continuous region:

,~.'L=O 1~°

~,~ p(E~, I~)dF,[ . :'"

~'"

)

(4)

The results obtained from these calculations of the absolute differential cross sections are shown in figs. 5 and 6 for nine states together with the experimental results. The integrated cross sections and the integration ranges, as well as the spin assignments are given in table 2. 4. Discussion and conclusion Present knowledge of the states in i s N is given in ref. 18) and we adopt this sequence of states. In general, both reactions studied excite the same states strongly. Since the four-particle transfer reaction preferentially populates particle-hole states, it must be assumed that these very strongly excited states have a x-particle y-hole configuration. The negative parity states up to 9.15 MeV are well understood. The ground state and the state at 6.32 MeV, both of negative parity, are hole states with a hole in the p~ or Pt shells, respectively 4). Both states are fairly weakly excited in both of the present reactions. Due to the high positive Q-value for these reactions, particles leaving the residual nucleus in the ground state could not be measured. The states at 5.27-5.29 MeV, which could not be resolved, are known to have positive parity. They are only weakly excited in both reactions. The unresolved doublet at 7.15-7.30 IVfeV,as well as the state at 7.56 MeV are positive parity states. Again, the excitation is moderate to weak. The ½+ state at 8.31 MeV is almost absent in both of the reactions studied. All these positive parity states most probably do have a rather pure lp-2h configuration which is difficult to populate in these many-particle transfer reactions. The states at 5.29 and 8.57 MeV, however, are strongly excited in a direct three-particle transfer reaction a), which indicates contributions from 3p-4h configurations. The next two states at 9.15 MeV could not be resolved in either experiment. It is well known is), however, that they differ in parity. This has led to the assumption

0

-

I

712°

24

0

6S

96

~

ongl. [~.m.]

72

2

9.155 MeV 5/2"

. . . . . . . .

120

~ ~ ~ "'1---~ ...................... 9.152 MoV 3/2" ~ ~ . - . / ~ . _~ ~

g.ls2. Q.ss~v

lo B ( 7Li,d)l~l

i

146

1111

Ex=9 8 ~ ¼eV

I

_

E x : 9.152÷9,155 MeV

I.

~ =7~56 ~ V

"

Fig. 5. Deuteron angular distributions for the population of states at 7.56, 9.152, 9.829, 10.7 MeV in the (TLi, d) reaction.

1

~ ' 1 lO;r

10'

102

10:

~

24

48

,~"

96

,,.

ongt. ~.~.]

72

%"

11/2" ~

120

.

.....

.

I

'

164

-

•

168

................

I

Ex=13.028 MeV

......

Fig. 6. Deuteron angular distributions for the population of states at 12.56, 13.028, 13.84, 14.11 and 15.37 MeV in the (TLi, d) reaction.

100

~1~"

1o_ .~. . .15. B(Li,d) N

T - - ' \ ~ ' -

~ .L~--I-~--.~.,~"

0

E

"/2

Id _-:'I':-~/

-..,

t-

0

C,

18N

121

TAeLe 2 The maximal differential cross sections and integrated cross sections E, (MeV)

J~ ")

o

It+ jr+ ||+ |+ ~+ ½+ |+ t÷ t|+ t|~

5.27

5.29 6.32 7.15 7.30 7.56 8.31 8.57 9.05 9.1518 9.1549 9,22 9.76 9.82 9.92 10.07 10.45

I tB(TLi, t)tSN (d~) ~l.t integ. m,~ (~b) range (~b/sr) (de8) { 380 100 { 260 260 48 480 1350

2000

1o.8oo 11.23

11.29

6- 94

65

80-165

|,

238

6-94

44

80-165

t-

537

6-94

119

80-165

|,t

496 146 686

6- 94 6-- 95 6-116

110

80-165

t

88

35-165

|

1450

6-116

} 285

35-165

~, t

2359

7-117

80

501

20-165

80

336

20--165

i, t

140

528

10-165

|

160

720

5-165

~,½

75 100 70 100 250 300

454 655 413 524 919 1366

5-165 5-165 5-165 5-165 5-165 5-165

| J~-

t+ ~.o,.~ t t÷ |+ t:>| i-

11.438 11.61

i+

11.76

~÷ |-

I1.87 11.94 ! 1.96 12.097

12.14 12.56 ¢) 13.028 13.19 13.84 14.11 15.37

jrl

this analysis

773

4OO 10.53 10.693 b) 10.700

t°B(TLi, d)tSN (da) a~, integ. ~ ~ (pb) ransc (pb/sr) (deg)

3100

3385

7-118

400

937

7-118

i, |

ei -

400

|+

tt (~-)

600 1500 600 2600 300 3400

2752

7-120

2766

7-120

7105

7-125

J~

") Ref. z s). b) Ref. 2-). °) R©f. ~). t h a t in t h e direct f o u r - p a r t i c l e t r a n s f e r reaction, m a i n l y t h e negative p a r i t y state a t 9.1518 M e V is excited, which c a n be r e g a r d e d as t h e lowest state with a m i x t u r e o f a 2p-3h a n d a 4p-Sh configuration. O n t h e o t h e r h a n d , t h e three-particle t r a n s f e r rea c t i o n s h o u l d excite t h e positive p a r i t y state at 9.155 MeV, as p r o p o s e d b y T s e r r u y a s).

122

w. KOHLER et aL

It cannot be clearly distinguished however, which state is populated in the t OB(TLi' d) reaction. The calculations of absolute cross sections would give a ratio of 3 : 2 for the 9.155 : 9.152 MeV states as given in table 2, due to the ratio of the spins. In a previous investigation at 6 MeV bombarding energy 19) the ] state was seen to b'. the most strongly excited one, in agreement with the condition of good angular momentum matching at this low energy. The state at 9.82 MeV ({r) is seen to be quite strongly excited in both reactions. Since the same state is strongly excited in the (TLi, ~) reaction a), spin and parity were assigned according to calculations by Lie and Engeland who proposed a 5 + state in that energy region 2o). From the four-particle transfer reaction one would rather assume a negative than a positive parity, whereas a compound nucleus reaction would be consistent with a spin of 5, but would not allow assigning a parity. The preferential excitation of high spin states in the 10B(TLi ' d) reaction can be responsible for the strong excitation of this state in the compound nucleus reaction. A negative parity state of spin {r in this energy region is also predicted by Zuker e t al. 2t). Beyond 10 MeV of excitation energy the strongest excited states are found at the energies 10.45110.53, 10.7, 11.94, 12.56, 13.028, 13.84, 14.11, 15.37 and 17.10 MeV. The maximum cross sections for all these excited states, populated in the different reactions, are given in table 2. Except for the states at 10.7 and 13.028 MeV, a significant difference can be seen from the selectivity of excited states. The 3p-4h states should be much more strongly excited in the (TLi, ~) reaction, whereas the four-particle transfer reaction mainly excites states which also carry a large amplitude of a 2p-3h configuration. Thus, in this respect, too, the two reactions, which seem to be of predominantly direct character are complementary to each other. Calculations which allow a much larger contribution of 4p-5h configurations are not available at the moment, but undoubtedly such configurations must contribute considerably in this excitation range. The (7Li, d) angular distributions have a remarkably symmetric shape. The calculations predict high spins for almost all of these strongly excited states in accordance with the picture of a grazing collision (fig. 4). The calculations of the absolute differential cross sections for the state at 10.7 MeV would give the correct values if its spin assignment were ~ instead o f ] . Thus it may be supposed that, at this energy, at least two states exist. A recent study of the I*C(p, 7) 15N reaction 22) shows a strong E2 transition from a state at 10.693 MeV to the 5.27 MeV (~+) state, with the conclusion that this new state, so far not reported in ref. 18), has a spin of ~+, in agreement with our assignment from the t°B(TLi, d) reaction. The interpretation of this state as a {+ state with a dominant 3p-4h configuration is supported by the 12C(7Li, 0e) reaction study also. A state with spin ~r is also postulated in a recent calculation published by Buck et al. 2a). The configurations of the strongly populated states beyond 12 MeV of excitation energy are not known, but it seems, from our spin assignments, that mainly high spin

lSN

123

states are populated (see table 2), which is a further proof that the multiparticle transfer reactions are particularly suited to the study of such states. For a new state at 12.56 MeV, also strongly excited in the lzC(TLi, 0c) reaction, a spin of ~ was proposed 3). The present analysis confirms tiffs assignment. Buck et al. z3) postulate a state with spin -~A at 13.15 MeV which can be identified with the known ~ - - state at 13.028 MeV. Furthermore, a state with spin ~ is predicted around 15.72 MeV which could also be the state at 14.11 MeV, the only one for which a ~ - assignment would be suitable from our analysis. There is, however, a strongly excited state at 15.37 MeV, for which our analysis would predict a spin Tt s rather than ~ , due to the error bars indicated. The same state is strongly excited in (~, ~') scattering 7). Generally speaking, it is observed again that different direct transfer reactions populate different states in residual nuclei. It seems, however, that some contradictions exist, because strongly excited states at 9.83, 10.7, 13.028, 14.11 and 15.37 MeV appear in the (TLi, ~) as well as in the (TLi, t) transfer reactions. Since the above mentioned states are more strongly excited in the four-particle transfer reaction, it is proposed that their population in a three-particle transfer reaction may proceed via a two-step process, where the target nucleus is first excited and subsequently the triton is captured. States of both parities could be populated by such a mechanism. On the other hand, the same mechanism, applied to a reaction with four-particle transfer to 11B, would also populate positive parity states with a somewhat reduced probability. The l°B(TLi, d) reaction can populate positive parity states with 3p-4h configurations, as well as negative parity states with mixed 4p-5h and 2p-3h configurations. On the basis of present knowledge the assignment of these states to rotational bands is not possible. It can, however, be stated that, if the high spin states belong to rotational bands similar to those known to exist in 160, the splitting of the multiplet components is much. too large for a weak coupling scheme 6). Thus, a similarity to 19F, where such a scheme is proposed, cannot be inferred. The comparison of the two reactions in discussion has shown that the compound nucleus generally populates high spin states, whereas the four-particle transfer reaction selectively populates states which have a pronounced particle-hole structure. The bombarding energy of 24 MeV, however, favours those states for which a reasonable angular momentum matching could be achieved. References 1) 2) 3) 4) 5) 6) 7) 8)

K. Bethge, J. de Phys. 32 (1971) 87 H. Schmidt-BOcking, G. Brommundt and K. Bethge, Z. Phys. 246 (1971) 431 I. Tserruya, B. Kosher and K. Bethge, Nucl, Phys. A213 (1973) 22 G. Mairl¢ and G..l. Wagner, Z. Phys. 258 (1973) 321 N. Anyas-Weiss et al., Phys. Lett. 12C (1974) 201 U. C. Schlottauer-Voos et al., Nucl. Phys. A186 (1972) 225 W. R. Ott and H. R. Wellcr, Nucl. Phys. A198 (1972) 505 E. Heinicke, H. Baumann and K. Bethge, Nucl. Instr. 58 (1968) 125

124 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23)

W. KOHLER et al. H. Schmidt-B6cking, Jahresbericht MPI Heidelberg, 1972 W. Kohler, Dissertation Universitat Heidelberg, 1974 (unpublished) G. Dietl, G. Gruber, H. Schmidt-BOcking and K. Bethge, Nucl. Phys. A250 (1975) 322 R. Book and H. Yoshida, Nucl. Phys. A189 (1972) 177 F. D0nau et aL, Nucl. Phys. AI01 (1967) 495 C. M. Perey and F. (3. Perey, Phys. Rev. 132 (1963) 755 K. Weber, K. Meier-Ewert, H. Schmidt-BOcking and K. Bcthge, Nucl. Phys. A186 (1972) 145 H. V. Klapdor et al., Nucl Phys. A2A4 (1975) 157 D. H. Thomas, Ann. Rev. Nucl. Sci. 18 (1968) 343 F. Ajzenberg-Selove, Nucl. Phys. A152 (1970) 1 R. L. Mc(3rath, Phys. Rev. 145 (1966) 802 S. Lie and T. England, Nucl. Phys. A169 (1971) 617 A. P. Zuker, B. Buck and J. McGrory, Phys. Rev. Lett. 21 (1968) 39 R. P. Beukens, T. E. Drake and A. E. Litherland, Phys. Lett. 56][$ (1975) 253 B. Buck, C. B. Dover and J. P. Vary, Phys. Rev. CII (1975) 1803