Magnetic moment of the 1h113 single-proton state in 141pr

~

NuclearPhysics A221 (1974) 211 --220;~) North-ttoUand Publishiny Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permission from the publisher

MAGNETIC MOMENT

O F T H E lh.~ S I N G L E - P R O T O N

S T A T E 1N 141pr

H. EJIRI, T. S H I B A T A a n d M. T A K E D A

Dept. of Physics, Osaka Univ., Toyonaka, Osaka, Japan Received 14 September 1973

Abstract: A magnetic dipole core polarization was studied by investigating a magnetic m o m e n t o f the

1117 keV lh~ single-proton state in ~4~Pr. The '~9La(~,2n?/)~4'Pr reaction was used to populate the 1h ~.tstate with spin aligned in a plane perpendicular to the beam axis. The magnetic moment was obtained by measuring perturbed angular distributions of the 972 keV gamma rays from the lh$ state. The y-factor of the lh$ state in ~4XPr was determined to be y ~ 1.30q-0.08. The isovector spin g-factor was deduced from the present result and the data for lh$ neutron states, It is 9~/y~° -- 0.45--0.1. The reduction is explained in terms of a spin-isospin (M1) core polarization.The isovector M I core polarization factor (nuclear M I susceptibility) is found to be one third of the M2 core polarization factor (nuclear M2 susceptibility) for the lh~ state. EI

NUCLEAR REACTION ~39La(~'2nT)~4'Pr' E=22 MeV; measured ly (O't'H)"

]

x'~aPr level deduced ,q, PAD method. Natural target.

I. Introduction Electromagnetic properties o f single-particle states in medium and heavy nuclei deviate greatly f r o m shell model values. This is because they are affected very m u c h by appropriate core polarizations, namely by admixtures of giant resonances associated with electromagnetic operators. Recently, we have studied magnetic quadrupole (M2) and electric octupole (E3) transitions from lh.~ single-proton states in nuclei with N ~ 82. The results i) clearly show that the M2 transitions are uniformly reduced by a factor geff(M2)/gfree (M2) ~ 0.22 due to a destructive effect o f the spinisospin core polarization 1-3), and the E3 transitions are uniformly enhanced by a factor eefr/e ,~ 3 due to a constructive effect o f the oetupole core polarization ~-3). These are polarizations with An = yes. It is interesting to study magnetic m o m e n t s o f these l h~L single-proton states and to c o m p a r e them with other electromagnetic properties. Here one m a y see an effect o f an M1 (za) mode core polarization with A7~ = n o .

We picked up for the present study the 1117 keV l h ~ single-proton state in a41pr with N = 82. This state is k n o w n to be o f quite pure single quasi-proton character from stripping and pick up reactions 4) and f r o m nuclear model calculations s, 6). F u r t h e r m o r e the electromagnetic properties have recently been studied by measuring M2 and E3 transition matrix elements 1). Experimental studies of magnetic m o m e n t s o f single-particle excited states in the rare earth region are scarce. This is mostly 211

212

H. EJIRI et al.

because of experimental difficulties in exciting these states and (or) in eliminating ambiguities due to extra-nuclear fields. A magnetic moment ,q~tNl of an excited state can be obtained by measuring the Larmor frequency ~oL of the spin L It is given as ,q#N I -- --~0Lh I, H

(1)

where FtN is the nuclear magneton and H is the magnetic field. The oJL is obtained by measuring a time differential perturbed angular distribution of deexciting gamma rays, provided that the spin of the excited state is aligned. Recently Ejiri et al. 7) have shown that (i, xnT) reactions feed preferentially medium- and high-spin states and the angular momentum is well aligned in a plane perpendicular to the beam axis. These features of the reaction are quite useful not only for spectroscopic study of excited states, but also for measurement of magnetic moments. Thus we used the 139La(~, 2ny)a41pr reaction to get the l h ? state with aligned spin, and measured the time distributions of the deexciting gamma rays at several pairs of angles. Here the quadrupole field, which would generally exist in rare earth nuclei, was eliminated by heating the La target. The details of the experimental procedure are given in the next section. The result and the analysis are presented in sect. 3. The observed moment is discussed in terms of the core polarization in sect. 4.

2. Experimental procedures The 1117 keV lh.~ state with z~ = 4.8 ns was excited by the 139La(0~, 2ny)X4tpr reaction with E~ = 22 MeV. The Osaka Univ. 110 cm cyclotron provided a bunched alpha beam with 2 ns width every 95 ns. The beam character is just suited for the present measurement of the perturbed angular distribution under moderate strength of the external magnetic field. The target used was a self-supporting, 10 mg/cm 2 La foil. It was prepared by rolling a small piece of annealed La metal. The foil was again annealed at T ~ 1000 °K. A crystal structure 8) of La metal at room temperature is a h.c.p. (hexagonal close packed) phase, and it changes at T ~ 500 °K to a f.c.c. (face centered cubic) phase with little quadrupole field. The La foil was heated up to T = 900 °K by mounting the target foil on a hot Ta filament with 50/~m thickness and 3 mm width. A piiometer was used for measurement of the temperature. The direction of the filament current was such that the electromagnetic force due to the external magnetic field pushed the filament towards the target, making good contact with each other. Gamma rays were detected with a 30 cm 3 Ge(Li) detector. Here filters tuned to the cyclotron oscillator frequency and its higher harmonics were used. Thus the RF modulation due to the cyclotron oscilllator was reduced to less than 3 ~o. Time distributions of the deexciting gamma rays were obtained by operating a 4096

141pr l h ~ SINGLE-PROTON STATE A

(a)

6~Go(Li )

(b)

213

H

A'

Fig. 1. Plane view (a) and schematic picture (b) of the experimental arrangement, n: direction of the incident ~-beam. AA': plane perpendicular to the beam axis (n). The spin of the compound state is aligned in the plane AA'. 1: magnet pole. 2: 139La target. 3: Ta filament. 4: mica insulator. 5: Ta beam stopper. 6: Ge(Li) detector. 7: brass target holder. 1: filament current. H: external magnetic field.

channel PHA with two dimentional mode (32 channels for energy and 128 channels for time). A time-to-pulse height converter was used with starting pulses from the RF signal of the cyclotron oscillator. A 40 cm 3 Ge(Li) detector was used as a monitor counter. Fig. 1 shows schematic drawings of the experimental arrangement.

3. Results and analysis A gamma ray spectrum is shown in fig. 2. Prominent peaks of the 972 keV and 145 keV cascade transitions and the 1117 keV crossover transition from the 1117 keV l h ~ state in 14[pr were observed. The magnetic moment was obtained by measuring the time distributions of the 972 keV gamma ray yields at two different angles. The yield of the deexcitinggamma rays is given as a function of delay time (t), angle (0) with respect to the incident beam direction and magnetic field (H). It is W(t, O, H ) = a e - "t ~, Av P~,(cos ( 0 - toL t)),

(2)

v

°~L = -OPN tt/h.

(3)

Here 2 is the decay constant and o~L = - 9 ~ N H/h is the Larmor frequency. Note that the interval of the beam pulses is much larger than the half-life in the present case. The magnetic field at the nucleus is given by H = f l ( T ) H o , where Ho is the external magnetic field and fl(T) is the paramagnetic correction factor 9). The latter is given as a function of the temperature T. The angle 0 is approximately written as 0 ~ q~- 0o where 0 o is a deflection angle of the or-beam due to the external field Ho and q~is the angle for the gamma detector with respect to the non-deflected beam line [the beam axis which we would have without external magnetic field ( H o = 0)]. An angular distribution

|

I 100

145kcV ,//~

I

I 200

273kcV

I

I 300

I

$1t kt~"

NUMBER

I 400

l

I

1

ell|keY

720¢(n,a )

OF CHANNEL

II Ill key

74Qc(n.~')

13'L, ( o( ,2 n l')'4'P,

I 500

~

~r

"r

,, 2 2 M e V

" .....

i 600

¢

i ~

,i

II

i.

!l

li

I

972 key

¥-~ ~r+ /

.... ~

"--'

5,.v

1117hrv

.i ...... 0 l , , v

~ .....

/

I .. ''''''v

700

i . . . . . . . . . . . . . . .

59Pr82

141

512" . . . . .

,,2

"'~--1

Fig. 2. G a m m a ray spectrum obtained in a time interval o f 10 ns, 13 ns after every other b e a m burst. T h e deexcitation s c h e m e is inserted.

~)11:5xl 03 ua

o

10 4

879

~4~Pr l h ~ SINGLE-PROTON STATE

215

of gamma rays following (i, xn~,) reactions is approximately written as W(O) = a [1 +A2P2(cos 0)]. The higher-order terms are empirically known to be very small ( < 5 Y/o) and they affect little the Larmor frequency of the oscillating pattern of W(t, O) [refs. 7, lo)]. Therefore we get a simple form for the difference

w(t, o, 02, H) -- w(t, 01, H)- W(t, 02, H) = ae->"z2A2[-sin ((--2~0Lt)+(--200)+4,1 +4,2)] sin (4,1-- 4'2). (4) We made four independent measurements (runs i-iv) of pairs of the time distributions W(t, Oa, H) and W(t, 02, H) for the following magnetic fields: (i) H o = - 17.4 +0.2 kG; (ii) H o = - 1 9 . 0 + 0 . 3 kG; (iii) H o = - 1 2 . 3 + 0 . 3 kG and (iv) It o = 19.0_+ 0.3 kG. The angles 4' 1 and 4'2 were 0 ° and 90 ° for runs (i)-(iii), and 0 ° and 45 ° for run (iv). The temperature for all four runs was constantly 900°+20 °K. This is high enough to keep the La target in the f.c.c, crystal structure. We checked the effect of the quadrupole field by observing the anisotropy of the gamma rays of present concern. It was nearly constant over a time range of ~ 20 ns. Thus the quadrupole field, if it were there, would only slightly affect the 09L which is of the order of 100 MHz for the present H. The observed differenccs A W(t, 01,02, H) are shown as a function of time in fig. 3. They clearly indicate the oscillating pattern as expected from the spin precession. The Larmor frequencies were obtained from least square fits to the data with two free parameters ~oL and A2. Here the beam deflection angles 0o were evaluated by observing shifts of the beam spot due to the magnetic fields. They were of the order of 10 °. Note that the angle 0 o is not essential for determination of the e~L and the fits with the two free parameters o~L and AE are as good as those with three parameters ~0L, A2 and 0 o. The obtained Larmor fre-

t(ns)

DELAY 20

30

TIME I0

0

aJL= 154-+ 13 MH=

.= 0

2+0.10 Z ÷

~o*0.05 Z

~"

0

o 0

~Z -0.05 i

~ -0.10 z ,

70

,

,

,

1

80

,

)

..I

90 NUMBER OF

~

)

~

)

f

I00 CHANNEL

,

~

i

~

I

I10

Fig. 3. A typical normalized difference of the time distributions of the 972 keV gamma rays from the 1h ~ state. This was obtained with the experimental condition ii (see text).

216

H. E J I R I et al.

quencies are ~c = 144+14, 154+13, 110_11 and 159+__14 MHz for runs (i), (ii), (iii) and (iv), respectively. The g-factors were determined from the measured Larmor frequencies by using g = --09Lh/(pNHofl(T)). We obtained values gfl(T) = 1.71 ___0.17, 1.68+0.15, 1.83-t-0.18 and 1.73+0.16 for runs (i), (ii), (iii) and (iv), respectively. The errors are mostly due to the statistical errors of the gamma ray yields. Thus a value gfl(T) = 1.74+0.08 was obtained from a weighted average of the measured values. We used a value 1.34 ___0.05 for the paramagnetic correction factor fl(T = 900+20 °K) by referring to both experimental measurement and theoretical calculation 9). The correction factor is rather insensitive to the temperature at the present high temperature. The Knight shift correction is 0.75 70 for La metal t~). We neglected an effect of the magnetic field induced from the filament current, which was only 0.3 ~ of the external field strength. Correcting for the paramagnetic factor fl(T), we finally obtained the g-factor g = 1.30___0.08,

(5)

for the lh~ single-proton state in 141pr. It should be mentioned that the measured value 0.065 +0.0075 for the A2 coefficient is about half of what we expect for prompt gamma deexcitations following (~, xn) reactions tz). The reduction might be due to the extra-nuclear field effect for recoiled nuclei which eventually do not end up at the symmetric center of the La crystal. 4. Effective g-factor and nuclear M I susceptibility

The present lh:~ state in 14tpr has been studied from stripping and pick-up reactions 4). These reactions show that this state is a pure (> 95 ~ ) quasi-proton state. Conventional model calculations 5, 6) including pairing, quadrupole and octupole interactions, show that the single quasi-proton amplitude is more than 95 ~o- Thus the g-factor can conventionally be written in terms of effective g-factors for the lh÷ single proton as follows: geff

cff--

1 z off

cffx

= gl ~-Ti-l,g~ --g, 1.

(6)

Inserting into eq. (6) free proton values g~ff(p) = 1 and g~ff(p) = 5.585, one gets gSchmidt(P) = 1.416. The measured value of g = 1.30+0.08 is very close to the

Schmidt value, and is in accord with the systematic feature found for other pure proton states ~3-15) w i t h j = l+-~. They are illustrated in fig. 4. Using a value ~6) g~fr 1.1 we get g~e f f t/g.,free = 0.59+__0.15. The reduction rate is the same order of magnitude as we expect from a spin core polarization 3). The g-factor [eq. (6)] for single-particle states withj = / _ 5 is rewritten as a sum of isovector (g_) and isoscalar (g+) components, 1 g =

+

.......

4l+2

(g~

ere r3+gs+)+

2 1 _ _ -1I-T- 1 , erf

4•+2

(gt-

-

eff',

r3-t-gl+)-

(7)

l*lPr l h . SINGLE-PROTON STATE

217 ,-~eff

IO

:a. 5

PROTON / ('r3=-I/

NEUTRON ~

'5

°

-/

gs÷ I

I

I

, 1',

I

.4,

,

-lOgs_"

Fig. 4. Magneticmomentsofpuresingle-proton states withj - l + ½. The Schmidt value is given by a solid line, and the experimental values are shown by closed circles. The value for the l h 9 state is the present value for ~ P r s 2 , and the values for the lg~_ and 1t~_ states are those of 1°~In6o [ref. t3)] and *lSc [ref. 14)l respectively. The values shown by crosses are guess values based on the data of the two-particle configuration states [ref. ~5)].

.

/. /-5

,'~- ,"..." "

'

Fig. 5. Isovector and isoscalar g, factors for the lh~ state determined from the experimental gfactors for the lh~ proton state in ~4~Pr and the l h ~ neutron state in XZ3Te. Here we used 6g~_ ~ --0. I v3. The errors shown by the shaded area are those due to the experimental errors in the g-factor. The Schmidt values (g]P and g ~ ) are indicated by arrows.

Here the effective ,q-factors, g,± _off = (,q~(n)+,q~(p)) °ff and g,~ err = (,q,(n)+,q,(p)) °", stand respectively for the r e n o r m a l i z e d spin and orbital ,q-factors. N o w we assume t h a t the core p o l a r i z a t i o n effects are very s m o o t h functions o f mass n u m b e r , a n d thus the , q ~ are a b o u t the same for nuclei with nearly the same mass n u m b e r (see below for the detailed a r g u m e n t on this a s s u m p t i o n ) . Then we get the values g~+ elf f r o m the observed ,q-factor for the present l h ~ p r o t o n state in ~ 4 ' p r a n d those t7) for the l h ~ n e u t r o n states in Te isotopes. The values g~_ af ~ - 4 . 4 a n d .q~f+f ~ 2.2 are o b t a i n e d f r o m the , q ~ and ,q,,;+ elf d i a g r a m as shown in fig. 5. Here we used values 15) af = 1.0 a n d ,q~Lf = - 1.2. I f we use values g~f+f = 1.05 a n d g~rf gt+ _ = - 1.11 suggested in the lead region ts), we get g~f_~ ~ - 5 . 2 a n d g~[+f = 1.8. The isovector spin g - f a c t o r is a l m o s t half o f the free nucleon value, indicating the large destructive effect o f the isovector spin core p o l a r i z a t i o n . O n the other h a n d the g~+ ar is nearly the same as the S c h m i d t value a n d there seems to be little isoscalar core p o l a r i z a t i o n . Similar reductions due to large isovector p o l a r i z a t i o n s have also been suggested for the M 2 ( m a g netic q u a d r u p o l e ) t r a n s i t i o n m o m e n t s ~' z) in the present mass region, a n d for M1 d i a g o n a l m o m e n t s in the lead region 3, 18). It is interesting to c o m p a r e qualitatively the present isovector M1 core p o l a r i z a t i o n with the isovector M2 core p o l a r i z a t i o n . Ejiri 2, ~9) a n d F u j i t a zo) have shown that the effective c o u p l i n g c o n s t a n t for the single-particle m o m e n t is a p p r o x i m a t e l y written in terms o f M L p o l a r i z a t i o n factors (nuclear M L susceptibility) as follows: g ar(ML) g(ML)

1 -

1

+F_(ML)+E+(ML)'

(s)

where F _ a n d F + represent respectively the M L p o l a r i z a t i o n factors (nuclear M L

218

H. EJIRI et al.

susceptibility) due to forward and backward correlations. [By putting F+ = F_ in eq. (8) one gets a value for the diagonal moment as discussed by Mottelson 21).] The value ffeff/9 for the isovector MI moment of the present lh~L proton state is #~f__r(M1)/gf~e(Ml) = 0.47__0.1. On the other hand the detailed analysis ~' 2) of the M2 "/ and the analogous first forbidden fl transition moments for the lh~.~ single proton states in N g 82 nuclei give #'__rt(M2)/g~C(M2) ~ 0.2+0.04. Thus we get the polarization factors F + ( M 2 ) + F _ ( M 2 ) = 4+0.7 and 2F_+(MI) = 1.1 +0.4. The M 1 polarization factor is about one quarter of the M2 polarization factor. The polarization factor (nuclear M L susceptibility) is simply given as F = aN, where ~ is the polarizability and N is the number of nucleons involved. The difference between the MI and the M2 polarization factors may partly be accounted for by the different number of nucleons participating in the two polarizations. The M1 polarization consists essentially of spin-flip particle-hole excitations from j = 1+½ to j = l - ½ orbits, while the M2 polarization is due to l hco jump excitations of all possible protons and neutrons. The number of nucleons for the M1 polarization is about (2jp + 1 ) + (2in + 1) and that for the M2 is about twice the number of nucleons in one hco shell. The former is about one quarter of the latter. Now let's try to evaluate an absolute value of the polarization factor. Using a simple polarization interaction HI = Zzzatr, we get the following nuclear M1 susceptibility (MI polarization factor) as in case of isovector E1 and M2 (L = 2) transition moments ~' 2, 19, 20); F.±(M1) = Z N iuj, (9) c~i = z,_~ I<.j' = / - ½ l l v a l l J =/+zl->[ 2 z E~ 3(2j + 1) '

(10)

where ~j is the polarizability of the nucleon in the j-orbit, and Nj = 2j+ i is the number of nucleons in the j-orbit. Here we assume for simplicity that the M 1 polarization is mostly due to spin-flip particle-hole excitations from j = l + ~- (sub) closed shells. (Note that the c o r e 1 4 ° C e of the present ~4tPr consists of lh¥ neutron closed and lg~ proton sub-closed shells.) The parameters AE and Z in eq. (10) can be obtained empirically as proposed by Bohr and Mottelson 3). The excitation energy is evaluated from the spin-orbit interaction obtained from nuclear scattering 3.22) as AE i -- 12(2/+1)A -~ MeV. The spin-isospin interaction strength Z,, is approximately given by an isospin interaction X, since the Majorana interaction is dominant in exchange nuclear interactions. The isospin interaction is obtained from a nuclear symmetry energy 3.22) V, = 100 tT/A. The reduced matrix element is I(Jl = l-½llz3trl[Js = i + ½ ) 1 2 = 4(1+1) 2l/(2l+ 1). Inserting these values into eq. (I0) we get F±(M1)~

4 ( 12+l p.n. 3A - ~ \)2 -t- 1+0.25!

-----g-A-~.

(11)

14tpr l h ~ S I N G L E - P R O T O N STATE

219

It is interesting that the M1 polarization factor (M1 susceptibility)does not depend on the shell orbits involved in the polarization. This can be explained as follows. The number of nucleons which participate in the polarization is approximately proportional to 2 l + 1. The polarizability ~j is rewritten as ~j = ( h i ) / A E i , where ( h i ) is the polarizing interaction energy, which is given by ( h i ) = 7.(2/3)(2l)/(21+ 1). 2 It is nearly constant (h j ) g -3-Z. Therefore the polarizability ~ is inversely proportional to 2l+1 because the energy cost A E j for the polarization is proportional to 21+ 1. No matter which orbits are involved in the polarization, the term Nj ~j is nearly constant. The polarization for the present nucleus (A = 141) is obtained eff free from eq. (11) as 2F± = 1.02. This leads to a value g.~-/gs= 0.49, which compares well with the experimental value. 5. Discussion

The present argument on the M 1 core polarization is based on an assumption that the core polarization is induced by a spin-isospin interaction H t = zzraa, and thus the effect is written in terms of the effective (renormalized) g-factors. In fact there is a tensor component 6kt = gp(aY2)~(2n) ½ as suggested by Bohr and Mottelson 3). It cannot be rewritten by the renormalized g-factor. Similarly there may be a term [o-Y3] 2 in the M2 transition moments, too. The contribution of the tensor term to the present g-factor is 6g_ = 10gp_/13. This amounts to about one fifth of the deviation of the gs from the free nucleon value according to a simple perturbation treatment of a 6 interaction 23). However one may not use a simple perturbation theory for M L core polarizations since M L core polarization factors are of an order of unity. The tensor term is considered to arise partly from a residual interaction H; = Z'z'~tro'Y 2 Y2- Since it couples with the main polarization interaction H t = Xzzaa, one cannot separate the tensor component from others. This problem remains for future work, and in the present paper we only say that about a quarter of the present M1 susceptibility might be attributed to the tensor term. The M1 core polarization effect can be rewritten in terms of admixture of an isovector MI giant resonance as in the case of M2 core polarization 1). The uniform effect of the isovector spin core polarization suggests existence of the MI giant resonance a few MeV above the average spin-orbit splitting energy. It is quite interesting to search systematically for the M1 giant resonance. We will present elsewhere the detailed arguments on comparison between M1 and M2 polarizations and the relation between M L giant resonances and the M L core polarization effects on magnetic moments. Note added hz proof." Strictly speaking the g~r__fdepends a little on the core, and the present cores 12STe and 14°Ce are not exactlyj = l+-2t closed shells. Detailed calculations, however, show that g~(14°Ce) is 3.4 ~o larger than that for 12STe, and eff gs_(Te) should be 8% larger than that given in eq. (11) f o r j = l+½ closed shells.

220

H. EJIR1 et aL

The authors would like to express their cordial thanks to Professors J. I. Fujita, M. Morita, K. N akai, M. Sano, K. Sugimoto, S. Yamabe and T. Wakatsuki for valuable discussions and encouragement. We thank Mr. M. Fujiwara for his help and interest. References 1) H. Ejiri, K. Satoh and T. Shibata, Phys. Lett. 38B (1972) 73; H. Ejiri, T. Shibata and M. Fujiwara, to be published 2) H. Ejiri, Nucl. Phys. A178 (1972) 350 3) A. Bohr and B. Mottelson, Nuclear structure, vol. 1 (Benjamin, 1969); vol. 2, to be published 4) B. H. Wildenthal, E. Newman and R. L. Auble, Phys. Rev. C3 (1971) 1119; T. lshimatsu et aL, J. Phys. Soc. Jap. 28 (1970) 291; O. Hansen et aL, Nucl. Phys. A l l 3 (1968) 75 5) N. Freed and W. Miles, Nucl. Phys. A158 (1970) 230; H. W. Baer and J. Bardwick, Nucl. Phys. A129 (1969) 1 6) H. Ejiri and M. Sano, private communication 7) H. Ejiri et al., Phys. Lett. 18 (1965) 314; Nucl. Phys. 89 (1966) 641 8) W. T. Ziegler, R. A. Young and A. L. Floyd, J. Am. Chem. Soc. 75 (1953) 1215 9) C. Giinther and I. Lindgren, Perturbed angular correlations, ed. E. Karlsson, F. Matthias and K. Siegbahn (North-Holland, Amsterdam, 1964) p. 356 10) C. F. Williamson, S. M. Ferguson, B. J. Shepherd and I. Halpern, Plays. Rev. 174 (1968) 1544 l l ) D. Zamir and D. S. Schreiber, Phys. Rev. A136 (1964) 1087 12) H. Ejiri, T. Shibata, A. Shimizu and K. Yagi, J. Phys. Soc. Jap. 33 (1972) 515 13) L. L. Marino, unpublished; 1. Lindgren, Alpha-, beta- and gamma-ray spectroscopy, ed. K. Siegbahn (North-Holland, Amsterdam) table, p. 1621 14) K. Sugimoto, A. Mizobuchi, T. Minamisono and Y. Nojiri, J. Phys. Soc. Jap. Suppl. 34 (1973) 158 15) T. Yamazaki et aL, Phys. Rev. Lett. 25 (1970) 547; S. Nagamiya et aL, Phys. Lett. 33B (1970) 574 16) T. Yamazaki et aL, Phys. Rev. Lett. 24 (1970) 315; H. Miyazawa, Prog. Theor. Phys. 6 (1951) 801 17) L. Vameste et al., J. Phys. Soc. Jap. Suppl. 34 (1973) 423 18) K. Nakai et aL, Nucl. Phys. A189 (1972) 526 19) H. Ejiri, Nucl. Phys. A166 (1971) 594 20) J. I. Fujita, Prog. Theor. Phys. 47 (1972) 523 21) B. Mottelson, Lecture note for the Nikko Summer School (NORD1TA, 1967) 22) G. W. Greenlees and G. J. Pyle, Phys. Rev. 149 (1966) 836 23) R. J. Blin-Stoyle, Proc. Phys. Soc. A66 (1953) 1158; A. Arima and H. Horie, Prog. Theor. Plays. 11 (1954) 509