Survey of electromagnetic properties of positive parity states in odd 1f72 shell nuclei

I

1 oE~4

[ I

Nuclear Physics A262 (1976) 317 - 327, (~) North-Holland Publishing Co., Amsterdam N o t to

be reproduced by photoprint or microfilm without written permission from the publisher

SURVEY OF E L E C T R O M A G N E T I C PROPERTIES OF POSITIVE PARITY STATES IN ODD I f t S H E L L NUCLEI J. S T Y C Z E N +, J C H E V A L L I E R . B HAAS, N S C H U L Z , P T A R A S " and M TOULEMONDE

Centre de Recherches Nuclbatres and Um~ervttb Lout~ Pasteur, 67037 Strasbourg, France Recewed 29 December 1975 Abstract: Expenmental transition rates B(M1) and B(E2) for m-band K" = ~+ translhons m ,,3, 4s. 47Sc ' 45Ti and 47.49 V have been systematically compared In the framework o f t h e pure rotational model, mtnnslc quadrupole m o m e n t s [Q0l and ],qg- 0 ~ [ ratios have been derived. Band mixing calculahons have been performed for the positwe parity states It turns out that the experimental data are well reproduced m these calculations with a deformatlon parameter corresponding to a m i n i m u m of the static potentml energy

1. Introduction

Several odd-A nuclei in the lower part of the l f~ shell provide evidence of nonclosure of the '~°Ca core through the occurence of low-lying positive parity states. These states arise from the promotion of an s-d shell particle to the lfl shell. The presence of, for example, J~ = 3÷ states in these nuclei can be easily explained in the framework of the Nilsson model. The Nilsson K ~ = ~2÷ orbital and the lowest orbital of the lf~ shell approach each other rapidly for increasmg deformation and thus allow appearence of low-lying core excited states. Already in 1971 Maurenzig 1) pointed out that the positive parity states in some 1f~ shell nuclei obey the J(J+ 1) rule and can be organized into rotational bands built on the J = ½and J = 3 proton or neutron hole states. In the 435c nucleus, the positive parity states were interpreted by Johnstone 2) to result from four-particle, one-hole (4p-lh) states projected from the lowest K ~ = ½+ and 3 ÷ Hartree-Fock configurations. This model was quite successful in predicting the decay properties of the K ~ = ~-+ and K ~ = ½÷ bands 3, ,~). However, such calculations of a microscopic character have been done only for 43Sc and are lacking for other nuclei. At the present time, there exists considerable experimental data on the positive parity states in 1f~ shell nuclei. In this paper the experimental transition probabdities obtained from the measured lifetimes, mixing and branching ratios in 43Sc [refs. 3-5)3, 45Sc [ref. 6)3 , 47Sc [refs. 7, 8)3, 4STi [refs. 9, 10)], 47V [refs. 11-13)] and 49V [refs. 14-16)] are systematically compared. Since the K ~ = ~-+ bands are not yet well characterized in the lf.~ nuclei, the comparison is done only for the + Permanent address. Institute of Nuclear Physics, Cracow, Poland " Permanent address Laboratowe de Physique Nucl6aire, Umverslt6 de Montr6al, C a n a d a 317

318

J STYCZEN et al

K" = 3 + bands. Indication of the deformation in these nuclei, is obtained from the transition probabilities in the framework of the pure rotational model. More sophisticated calculations can be performed using the strong coupling model Such calculations were performed for the cross-conjugate nuclei *TV-49Cr and 49V47Ti. They are fairly successful in reproducing the energies of the negatwe panty states 17) and in explaining their electromagnetic properties t s). For these states. the presence of many closely spaced I f and 2p subshell orbltals and a strong Coriohs coupling destroy the original J ( J + 1) band structure which, however, remains for the positive parity states. The same model was recently used to study possible regions of stable deformation of positive parity states of the odd nuclei in the lf~ shell 19). In strongly deformed nuclei, two regions of prolate and oblate stable deformations were obtained, but a potential having the positive deformation alone can reproduce the observed energy variation with J(J+ 1) (see sect. 3). In the present work the strong coupling model is used for a detailed study of electromagnetic properties of the positive parity states in each nucleus for which there exists sufficient experimental data. 2. Experimental transition strengths and the pure rotational model The energies of the positive parity states observed in I f,~ shell nuclei follow quite nicely the J(J+ 1) rule (fig. I). In each nucleus shown m fig. 1, with the exception of 43Ca, lifetimes have been measured for a fair number of positive parity states as have 7-ray mixing and branching ratios for many transitions between these states. From these experimental data, the reduced transition probabilities were calculated using the relations B(M1) = 0.0569E-3R [z(l +x2)] -1/~0z ,

(1)

B(E2) = 816E-SR [z(l +x-Z)] - 1 e 2" fro*,

(2)

where the transition energy E is in MeV and the lifetime z in ps. Here, R and x are the branching and the mixing ratios, respectively. In order to observe enhancements or inhibitions of the M 1 and E2 transitions compared to the single particle estimates, the transition probabilities are also given in Weisskopf units which are obtained by dividing relations (1) and (2) by 1.79 and 0.0594 A'~, respectwely. Upper and lower limits for the enhancements and inhibitions were calculated taking to account the extreme values of z, x, R and E. The B(E2) values obtained for the K" = 3+ bands in 4.3. 4-5, 4.75c ' 45Ti and 47. ,9 V are given in table 1. It should be pointed out that all the B(E2) are strongly enhanced over the single particle estimates. Providing that t h e / C = 3 + bands are pure, the B(E2) value for a tra~:~ltion between two members Ji and Jf of a band of projection K is given by B(E2) = (5/16 rc)e2Q~ (Ji2KOiJfK) z

e 2 • fin 4.

(3)

ELECTROMAGNETIC PROPERTIES

319

10.1

_/

.

.

.

.

.

JJl ,,/

,~ 4t

i

/

,/" /'"

,, V/

"° ,,,'{SSc

. / " ."so /J

i" /

0.5

/ i r /ZZ

1

1 ~

,0 0.5

3/25/2 7/2 9/2 11/2 13/2 3"(3".I)

15/2

Fig 1 Energies o f the members o f the K ~ = ~ ~ baud m 43Ca, 43, 4s, 47Sc ' 45T1 and 47, 49V For the sake of the presentation the energies for each band were normahzed to au arbitrary value of the ordinate. The full hnes connect states w,th unamb]guous spin ass]gnments

I

I

I

I

I

I

I

I

Fig. 2 Absolute value o f t h e intrinsic quadrupole m o m e n t derwed from eq (3) for different J, -~ Jr transitions In the upper part of the figure, the experimental B(E2) values for the Sc Isotopes were used to calculate PQoI- In the lower part of the figure, a sohd hne connects the values obtained using the rotauonal formula (eq (3)) and the theorehcal B(E2) values obtained for 45Sc by the strong couphng model

The intrinsic quadrupole moment Qo is related to the deformation parameter fl in the following way:

Qo = (3/v/5zt)ZR2fl(1 +0.36 fl) fm 2,

(4)

where Z is the atomic number, R = 1.2 A ~ and fl = 1.05 ~. For every given B(E2), the absolute value IQol was deduced. The results are summarized in table 2. The fact that the weighted average value PQoJavdoes not change appreciably from one nucleus to another gives evldence for a simdar deformation for all of these nuclei. However, it should be noted that Qo is not strictly constant in each nucleus (see upper part of fig. 2). The B(M I) calculated with relation (1) are given in table 3. In the N ilsson model, B(M 1) is related to the intrins]c ~¢r and rotational 9R gyromagnetic factors by B(M1) = (3/4 g)K2(gr--gg) 2 (J, IKOIJfK) 2

!a~.

(5)

320

J. STYCZEN et al. T.XBLL 1 Expertmental E2 strengths (W.u) for K ~ = 2~+ bands

j, _.~ j f

,,35c ~)

45Sc b)

4.7Sc ¢)

,5T1 d)

47v ~)

2/

421 20-13

38+35 -19

43-5.7 -29

61+26 -18

< 1 3 x 103

~ __) 2~

24+22 -12 12_+~

19"27

< 42x102 11+~

+1.7 24_1o 18*6_

+67 12_it 22_, t+t7

<45>,:102 34 ,25_1s

2~~ .7 ~

--lo 12:3

~--) ~

5"- 4

5+_3

11 +22_ .7

-~ ~2

14-_~

14+-6

20_-23

Z[._. 9 2 2

+33 31-2o

--* '72

18+_4

a~_ 2 ~ J,! 2 -92 ~) h) c) d) ~) f)

E2 E2 E2 E2 E2 E2

49 v t) 23.35 -is < 34 15+4_ <24 2X'30~-14

9-18

< 77xl02

23_+ 1 49

34_ 18

+32

< 45x102 13-~s

strengths were ~alculated strengths were calculated strengths were calculated strengths were calculated strengths were calculated strengths were calculated

using data from refs 3-s) m the preceedmg paper 4) using data from refs .7. s). using data from refs 9. 1o). using data from refs ~ -~3) using data from refs 14- t6)

TABI F 2 Intrinsic quadrupole moment Qo and deformation parameter 6 derived from the experimental B(E2) values for the K ~ = 5 + bands Iaol (b) ") J, ---}Jf a3Sc ~2~

aSSc

a.TSc

45Tt

47V

a9V

~

0.80+028

1 13+-0.33

1.29+0.49

1 35+0.23

< 607

1 00+-028

~ --* ~z

1 10+033 0 8 9 +. 0 1 1

0.96+-042 093-1-008 .

<4.44 . 093+026 .

1.12_+0.27 I 1 2 + 0.1 6

1.38+067 133+0.38

< 131 106+014

~_~2 ~ 2

0.60+019_ 080+-0.11

069+026_ 078+017

113+043_ 1 11+-0.31

<567 1.33+038

<135 1 33+-049

~---, 2 ~ --. _7 2

1.87+064 080+-007

119+051 0 9 8 +- -0 2 2

~

x.~_ ~ L1 2 2 9 2

<916 1.18+045

< 7.71 0 7 0 + 0 15

IQol,v

082+005

088+006

1 01+023

1 17+__0 11

1 34+0.25

1 0 7 + 0 12

6

0.25 + 0 0 l

0 2 6 + 0 02

0.29 + 0 06

0 33 +_0.03

0 34+-0 06

0.28 + 0 03

a) The errors on Qo were calculated with symmetrtzed errors on the B(E2) values.

E L E C T R O M A G N E T I C PROPERTIES

321

TABLF 3 Experimental MI strengths (10 -3 W.u.) for the K" = ~+ bands J --, Jf

'3Sc ~)

"~Sc b)

,7Sc ~)

45T1 d)

,7 v ~)

,9 v f)

---} a2 2 -o ~ 9~ ~ -* ~

11 _+5 30_+t94 14+5_ 106+- - 18

13_+5 14_+45 7+~ "~3 +23 ~ -14

13_+1~ < 34

25+6 27_*~ 16+2~

< 79 27_2~

22_*~ 24_+7 28-44,s

7

"- f) M 1 transmon strengths calculated from the same respective references as gwen m the footnotes for table 1 TABLF

4

Values of Igx - gRI derived from the experamental B(M 11 values for the K" = 23+ bands

LqK-gRIa) J,-*4 43Sc

4SSc

47Sc

45TI

47v

49v

2~2 ~ 7_.,~ ~_..7 ~--*-g2

0.37+__008 0.55+010 035+_0.06 0.91+008_

041+008 037+005 035_+0.08 054+0.13_

0464-_014 <0.56 < 1.96

056+0.07 052+009 044_+013

<099 0.54+018 <(174

053+008 047+007 058+022

IgK--gRI,v

051-+013

0.39+004

0.46_+0.14

053+0.05

054+0.18

050--005

m

a) The errors on the Ig•-gRI ratios were calculated with symmemzed errors on the B(M1) values

In table 4 the absolute values of ]gK--gR] deduced for each B(M1) are presented. As for the IQ0[ values, the IgK--ggl factors are nearly constant.

3. Strong coupling model Properties of the positive parity excited states in the l f~ nuclei were calculated using the strong coupling model which has been recently apphed to find posstble regions of stable deformation for these states in all the odd nuclei 19). To facthtate the calculations, an inert 36S core was employed for the odd-Z nuclei and a 36Ca core for the odd-N nuclei. Details on the model as well as explicit relations for the electromagnetic transitions are given in ref. 2o). The parameters used in the present band mixing calculations are shown in table 5. The C- and D-parameters of the Nilsson model Hamiltonian were estimated from the single particle energies, as deduced from the 3 9 K and 39Ca energy spectra 21). The values of the deformation parameter correspond to minima of the total groundstate energy calculated for each nucleus as shown in ref. 19). It is seen in table 5 that the deformation parameter varies little and remains fairly close to that calculated from the intrinsic quadrupole moment with the assumption of a pure Nilsson model

322

J STYCZEN

et al

TABLE 5 Parameters used m the band mixing calculations Parameters a) Nucleus

6 43Sc 45Sc 47Sc 45Ti 47V

0 0 0 0 0 0

49V

h2/2J (MeV)

22 25 20 25 26 22

0 0 0 0 0 0

a) R = 1.2At'~ fm, 9 R =

075 060 080 065 065 065

C (MeV)

D (MeV)

- 2 75 -2.75 -2.75 - 2 75 -2.75 -- 2 75

-0 -0 -0 - 0 -0 -- 0

35 35 35 35 35 35

e

gt

1 1 1 0 1 1

1 1 1 0 1 1

q~ 5 5 5 - 3 5 5

58 58 58 83 58 58

Z/Aandhw o = 41 A-1~3 MeV,

TABI E

6

Calculated and experimental m a g n e h c dipole m o m e n t s for the K" = ~+ 2 band-heads #(nm) Nucleus

~) Ref 24)

theor

exp

43Sc 4SSc 47Sc '*STi 47V "~9V

0.11 0 09 0 10 1.20 0.09 0 11

+ 0 348 + 0.012 a)

b) Ref. 22)

¢) Ref. 2a)

+0,35 +0.05 b) +0.98 + 0 24 ¢)

(table 2). The rotational constant parameter h2/2J w a s used as a free parameter. It can be seen that its final values are closed to the averaged slopes of the curves versus J(Jq- l ) plotted in fig. 1. The calculated energy spectra for the positive parity states in 4SSc and 49V are shown in fig. 3 and are compared with the experimental spectra known for these nuclei The agreement is fairly good, though the calculated energy separation between K" = ½+ and K ~ = ~+ bands is larger than that observed experimentally. The decoupling factor for the K = ½ band was calculated to be - 0 . 5 4 and - 0 . 7 0 for 45Sc and 49V, respectively. It should be pointed out that these values correspond to a positive deformation. For a negative one, a large decoupling factor was found and consequently pairs of states which do not exhibit the J ( J + 1) energy dependence are predicted. An example is given in fig. 4 for 4aSc. The values of the deformation parameter correspond to the two minima of the static energy 19). In table 6 the calculated and experimental values are reported of the magnetic dipole moments for K ~ = ~+ band-heads in the investigated nuclei. G o o d agreement

ELECTROMAGNETIC PROPERTIES 2Y

2~

(1 S}

A

>(D Q: UJ Z UJ

2K

323

2Y

11

9

1

(13)

13

3

11

7

1

~

2Y

2K

15

3

11

1

9

1

13

3

7

1

(13}

(11) 5

9

9

1t )

7 7

3

5

7

3

5

3

3

3

5

3 EXP

1

SCH

5

3

3

3

3 EXP

45Sc

SCH /.9 V

Fig 3 Experimental and theoretical (strong couphng model) positive panty level schemes for the 45Sc and 49V nuclei

can be noticed for 45Ti. The agreement in the case of the Sc isotopes is not satisfactory. However, as can be seen in fig. 1, the K" = :~+ band-heads of these nuclei are appreciably lower than what one would obtain by extrapolating the J(J+ 1) curve to J = ~. This may indicate a configurauon mixing in these states which is not being accounted for in the present model calculations. The B(MI) and B(E2) values calculated for the 43, 45, 4 7 5 c ' 45Ti and 47. 49 V nuclei are compared with the known experimental data in tables 7 and 8. Some of the experimental B(M1) and B(E2) values are known with large errors, and this makes the comparison not very convincing. In other cases, however, the errors are relatively small (e.g. 43, 4 5 5 c ' 45Ti) and the agreement between theory and experiment is satisfactory. In the upper part of fig. 2 [Qol is shown derived with eq. (3) for different J, --, Jf.transitions using the experimental B(E2) values for the Sc isotopes. An identical calculation has been performed using the B(E2) obtained in the framework of the strong coupling model (see lower part of fig. 2). The small variations of IQol due to the mixing of different bands are well reproduced. 4. Sign of the deformation

The positive sign of the deformation parameter has already been suggested by energy spectra for 43Sc (fig. 4) calculated for negative and positive deformation parameters in the framework of the strong coupling model. However in this calcula-

324

J STYCZEN et al

~3Sc 2.T

2K

13 5 15 3

3 1 3

2~

1

'

2J"

2K

15

3

11

1

(15)

03)

3

(11) 9

9

1

13

3

? 11 5

1 3 1

9 3 1

3 1 1

7

3

5

3

3

3

11 9

5 7 3 5 1

1 5 7

1 1

3

~--0.25

,

EXP

~i =0.22

Fig. 4 Comparison of the experimental and theoretical energy spectra calculated for negatwe and positive deformauon parameters m 43Sc

tion, a weak band mixing has been found, thus the sign can be established using the pure rotational model. Knowing the magnetic moment of the I ÷ 'state and the sign of the multipolanty mixing ratio for the in-band transitions, it can be shown that with the Rose and Brink convention 25) the following relation is fulfilled: sign x -- - sign gr-g~_

(6)

ao

The magnetic moment of a deformed excited state can be written as 26) l~ = gRJ+K2(gr--.qR)/( J + 1)

n.m.

(7)

Thus in the case of 45Ti, since g~ = Z/A = 0.49 and p~, = 0.98 n.m. [ref. 23)], the sign of gr--gR should be positive. The sign of x was measured as negative lo). Therefore relation (6) wdl be fulfilled when Qo has a positive sign. The same procedure carl be applied to 43Sc and a positive deformation parameter is also obtained. Indeed for this nucleus the sign of the mixing ratio is positive s) and the gK-g/~ sign deduced from the magnetic moment measurement 24) is negative. It is seen in table 6

~

121

~

7

7

~

~

85

190+32

94

--' ~2

102

15

+32

162-28

4 29~ 280_175

73 46

38

+47

129_2o

42_23

115

theor

-

88 55

-

214_ao 8 1 0 6-~

~ 199

179_,15

43Sc

~19o

exp

--

+40

60_26

27±8 14±7

23+10 _

exp

,,55c

91

82 65

57

theor

126_49

+73

+128

131 _+55 87 - 17o 66

57_+~

+251

115_ 91 +25 119_19

360_18o

+33~

exp

45Sc

220_ 8o < 4 25 × 103

--

138

142 26

108 62

78 61

122

170

theor

Experimental E2 strengths (e 2 •

52

79 50

54_17 25+ 9

~25

2 0 _+ 9

theor

exp

~

"-* 2

---*

__~

~

~,

~

Jr

J,~

J, -~ J,

,,35c

TABI I 8

67

64 34

41

theor

48_+2° 29 +37

44 -129

exp

,*ST1

53

48 35

33

theor

+,*3 48_29

< 14×102

exp

47v

432_293

+.o

exp

`.7Sc

84

12

94

43

66

33

81 51

102

theor 579 16s

104_+209 62 187 +21° 73

233 ~_1~ +60 168_,,o

+ 247

exp

4STi

179

41

163

57

85 138

92

132

217

theor

2

199

37

202

155 85

88

111

171

243

theor

~z'

99

89 68

62

< 254

160_43

+ 376

246_1s s < 364

exp

49V

52

363~33as

141

24

148

110 64

60

81

173 127

theor

82

75 +78

50_31

51

theor

43± 12

,,9V

07 249_ 414a < 8 18 x l03

bands

exp 39~- 113 1

~+ bands

theor

K ~ =

< 4.49× 10 ~ 343_+252 I S0

120_~677 to6 +,6s 226_117

< 12 5 x 103

exp

47V

and values deduced from the band mixing calculations for the

< 420x103 l l l _,81 sa

fm`*)

< 60

24_12 +2,*

exp

,,7Sc

Experimental M1 strengths (10 3 ,u2) and values deduced from the band mixing calculations for the K ~

TABLF 7

t"

r.~

O

7¢

© ~r > 0 Z rn

~

326

J STYCZEN et al.

that the magnetic m o m e n t s for the ~+ states of*3Sc and "7Sc are not well reproduced in the strong coupling model. H o w e v e r using the g K - - g R factor deduced from the experimental B(M1, ~+ --. ~+), an empirical magnetic m o m e n t value can be calculated m framework o f the pure rotational model by means o f f o r m u l a (7). The values obtained # = 0 . 4 0 + 0 . 0 7 and 0 . 2 6 + 0 . 1 3 n.m. for "3Sc and '7Sc, respectively, are close to the experimental quantittes (see table 6). In the same way a value # = 1.24+ 0.06 n.m. is calculated for the *STi nucleus which is in g o o d agreement both with the experimental and the strong coupling model data.

5. Conclusions In the previous section it was shown that the k n o w n experimental data on the positwe parity states in I f I shell nuclei are in general well reproduced in the band mixing calculations for the positive deformation parameter. The present calculations were done with the same C and D Nilsson parameters in all the studied nuclei whereas for the positive deformation parameter the a d o p t e d value corresponds to the very m i n i m u m o f the static energy in each investigated nucleus. Even small variations in 6 significantly m o d i f y the transition rates. However, the aim o f the present w o r k was not to reproduce exactly the experimental data by changing the parameters but to show that the results o f the b a n d mixing calculations agree quite well with the experimental data for all the l f; shell nuclei for which the positive parity bands were investigated. Moreover, the positive sign o f the deformation parameter, suggested by the energy spectrum calculations, has been deduced from experimental transition probabilities and magnetic moments. We would like to thank Dr. A. Pape for critical reading o f the manuscript.

References 1) P R Maurenzlg, Proc. Int Conf on the structure of lfT, 2 nuclei, Legnaro, 1971. ed R A Rlcct (Edttnce Composmon. Bologne, 1971) p. 469 2) I P Johnstone, Nucl Phys. All0 (1968) 429 3) J, S. Forster, G C. Ball, F lngebretsen and C F. Monahan, Phys. Lett 32B (1970) 451 4) G C Ball, J. S Forster, D Ward and C F Monahan, Phys Lett 37B (1971) 366 5) G. C. Ball, J S Forster, F. Ingebretsen and C. F. Monahan, Can J. Phys. 48 (1970) 2735 6) M Toulemonde, J Chevalher, B Hass, N Schulz and J Styczen, Nucl Phys A262(1976)307 7) M. Toulemonde, L. Desch~nes, A Jamshi& and N. Schul7, Nucl. Phys A227 (1974) 309 8) V. Barct, F. Brandohm and M Morando, Nuovo Clm IIA (1972) 1 9) P BlasL M Morando. P. R. Maurenzlg and N Taccetl, Nuovo Clm Lett. 2 (1971) 63 10) J Kownackl, L Harms-Rmgdahl, J Sztarkler and Z. P Sawa, Phys. Scnpta 8 (1973) 135 11) N Schulz and M. Toulemonde, Nucl Phys A230 (1974) 401 12) P. Blasl, T Fazzmt. A. Glannatiempo, R B. Huber and C. Stgnonm, Nuovo Clm 15A (1973) 521 13) L. Mulligan, S. L Tabor, L K Flfield and R. W Zurm~ahle,Bull Am. Phys Soc. 20(1975) 732 14) S L Tabor and R W Zurmuhle, Phys. Rev CI0 (1974) 35 15) B Haas, J Chevalher, J. Bntz and J Styczen, Phys Rev. Cil (1975) 1179 16) P Blasl, M. Mando. P R Maurenzlg and N Taccetl, Nuovo Cim 4A (1971) 61

ELECTROMAGNETIC PROPERTIES 17 18 19 20 21

327

B Haas, P Taras, J. Styczen and J Chevalher, Phys. Lett 52B (1974) 146 B Haas, P Taras and J Styczen, Nucl. Phys A246 (1975) 141 B Haas, J Chevalher, A Kmpper, J Styczen and P Taras, Phys. Lett 61B (1976) 141 B Haas and P Taras, Can J Phys. 52 (1974) 49 R A Ricci, In Proc lnt School of Physics Enrico Fermi, Course 40, ed M. Jean and R. A Rlccl (Academic Press, New York, 1969) p. 126 22 D B Fossan and A. R Polettl, Phys Rev 168 (1968)1228 23 B Haas, A. Chevalher, J. Chevalher, C Gchrmger, J C Merdmger, N Schulz, J Styczen. P Taras, M Toulemonde and J P Vlvien, Phys. Rev C12 (1975)1865 24), R J Mitchell, T V Ragland, R. P Scharenberg, R E Holland and F J Lynch, Bull Am Ph)s Soc 20(1975) 1163 25) H J Rose and D M Brink, Rcv Mod Phyb 39 (1967) 306 26) O Nathan and S G. Ndsson, m Alpha-. beta and gamma-ray spectroscopy, vol I, ed K Slegbahn (North-Holland, Amsterdam, 1965) p. 601