Systematics of K-Isomerism

S Y S T E M A T I C S O F K - IS O M E R IS M M. S. RAJPUT AND M. L. SEHGAL

Dk p a h t m e n t of PHyaTcs, AJjIOABH IVIUSLIM XJn iv k iis it t

Al ig a r h, U.P. Ix d ia

(Received

ABSTRACT.

have been eompdod. From tho syateinatie study of A'-forbidden tran.sition in the m:ias region m < A < 190, and A > 230, it has been found tlmt log of hindrance factor per dc'gree for- bidctcnneSBof tho transition decreases with the increase in the value of degree of forbiddennoss ol the transition.

59

I N T R O D U C T I O N

No rigorous tlioory lia.s so far boon clovelopod for tho inodium and hoavy nuclei ( A > 150). which explains all their properties. Shell raodol, (Mayor and Jensen, 1052), ha.s been found to explain some of the observed properties of those nuclei with certain mass nnmhors. The general properties of those nuclei indicate that nillective nucleon motion plays an important part. Tho shape of tlie nuclei m this region is deformed. (Nathan and Nilson, 1965; Mottelson and Nilson, I.I59). Innou-sphcrical nuclei, a simplotypo of excitation due to the rotation of the niiclous in spaco takes place without changing tho .symmetry. Tn this region (100

^ ^ A > 230) at low excitation energies, the nuclcAr spectra shows rotational bands. For each rotational hand the component of total angular womontnm along tho symmetry axis i.s called £ . This is characteristic of intrinsic

<onfiguration, associatod with that band. Tho gamma transitions between dif­

ferent rotational bands depend also upon tho change in quantum nnnibor K, in addition to the change in spin and parity, whore,

A / > A A ,, (I)

Tho AT-selection rule is obeyed strictly when N is a good quantum number,

^•0., when tho internal as well as the rotational motions are independent of 0ach other. Actually there is a coupling between these two forms of motion and is only an approximate quantum number. Therefore the JT-selection rule results in decreasing the transition prol abilities rather than in completely forbidding the transition. The degree o f forbiddenness o f the transition is given by,

| A iT | -£

537

538 M. S. Majput and M. L. Sehgal

whore L is th<^ angular moiuontuin caxTioil away by tho radiation. In this invoati- gation we are i]\t«;rcsted in the systematics of the /iT-forbiddon transitions. The (lata on A"-forbiddou transitions liavo boon compiled to correlate) the A"- forbiddonnoss with tlio hindrant*o hietor.

All the oxpcrimontal data on tlu^ AT-for}>idden transitions have boon colloc^totl from various publications available Tocontly. The data is prosontod in table J Tho v^arious’ (*ohimns are self explanatory. Wo dofino the hindrance factor H.F.,

H.F. T*|Expj T4rS.PT)

where T^ ((^xp) is tho experimental half life of tlie state after applying conversion coofficiont and other eorroctions and (S.P.) is tho value of the. half life prodicbMl by tlio single particle model, (Blatt and Weisskopf, 1952).

A N A L Y S I S O F D A T A A N D D I S C U S S I O N

Hie oloctromagnotic transitions, forbidden by the AT-aolection rules, hav(^

boon fouivl to have half lives ranging from few microseconds to few hours. T1

‘ highly forbidden transitions, (Burduo et al, 1066; Borgroon et al, 1057), ocumrs in jjfiso half life of tho 1143 koV state from wliieh 57 koV transition originabwl is 5.5 hours. This giv(*s a hindranec factor 10^® as compared with tho singt>

partitilo ostimato. Recently Burdue et at (1066) havo discovered some more 8“ isomeric states giving A-forbiddon transitions having hindrance factor 10^^

to 10^^ in tho mass region 170 ^4 184.

Curtis Miclud (1064) siiggi‘>sted that tho parity mixing may bo rosponsiblo for the hindrance of A’ -forl>iddou transitions. I f tho spin and parity change in a parti- (udar transitiim allows tlio omission of plioton of given multipolarity then tln^

parity mixing allows a photon (jf multipolarity 31 ^ to bo also emitted. It was 8(iggcstod by Curtis Mioliel that tho parity mixed transition may bo dotoHtvd indirectly from the polarization o f tho radiation.

Goldhalicr and

(1066, 1967) moasurod tho A-subsholl conversion

cooffici(mt for the 57 koV transition in and they found that tho L

I)-

sholl conversion coofficionts are anomalous and tho oxp(rimontal results can he

explained if one considers this transition as 90.5% and 9.5% Law'son and

Segal (1966) and BloumlHirg et al (1967) pointed out that tho parity mixing is not

the explanation for tho doiayodness of tlioso transitions. Lawson and Sogal

(1966) also pointed cut that tlie soloction rules, tliat inhibits the emission of Aj

radiation, must also effect tho decay of tho stato by radiation. Recently

polarization experiments o f Pauli et al (1967) and Bloumborg et al (1967) have

rovoal(xl that tho possible explanation of tho anomalous L subsholl conversion co-

efBcionts o f 57 koV transition in Hf^®® and 1084 keV transition in Lu^’ * is not

Systematica of K-isomerism

tfu)

parity mixing. They have suggostod that fhit . tration offocts. Tlio ponotratif>n f *** ^ f o , „ w « „

539

2 4 0

V —•«

F/guro 1. Vibration of (log H.F.)/v with r for different multipolo transitions

Borggron

(1957) have suggostocl that tho isomoric^ staton wliioli dooay

’Via /f-forbidden transitions arc two quasi-particle states. Tho ('oupliug boiwoen cso two is responsible for tho TiT-isomorism. However tlio aggreemont between

^0

experiment and tho theory is not good. At present it is very hard to umlor-

Q-ud tho hindrances of £^-forbidden transitions in the absence of a rigorous theory.

5 4 0

M . 8. Rajput and M . L. 8ehgal Table I /jC-forbiddon Transitions

Odd-Nuclei

SI.

No. Nucleurt

Gamma- ray energy in

KeV Initial State

I K 7t{NNsA) Final State

I

1. Tbioi 361 7/2 7 /2 - (5 2 3) 5/2 3 /2 4 (4 1 1) 1 4.2 (7) 1.2

284 7/2 3/24-(4 1 1) 1 1.6 (6) -

2. 152 7/2 7/2--(5 2 3) 7/2 l/2 -f(4 1 1) 2 1.7 (9) 3

176 ft 5/2 ]/24-(4 1 1) 2 1.6 (8) ft

3. Tmioo 241 7/2 7 /2 - (5 2 3) 7/2 l/2 + (4 1 1) 2 1.7 (9) 4

261 - .5/2 l/2 + (4 1 1) 2 1.6 (8) -

4. 290 7/2 7 /2 - (5 2 3) 7/2 1/24(4 1 1) 2 5.1 (8) 3

308 5/2 1/24(4 1 1) 2 4.8 (8) ff

5. Yhi73 395 3/2 l / 2 - ( « r. 1) 5/2 5/2 + (5 1 2) 1 5.4 (5) 5 6. 123 6/2 l/2-~-{6 4 1) 7/2 7/2 + (4 0 4) 2 2.5 (8) 6 7. 345 7/2 7/2 + {4 0 4) 5/2 l / 2 - ( 5 4 1) 2 2.6 (8) 0 8. H,.183 382 9/2 9 /2 - (5 J 4) 7/2 5/2 + (4 0 2) 1 2.24(6) s

236 - 9/2 5 /2 4 (4 0 2) 1 7.6 (6) 8

9. 72 9/2 9/2~^(5 1 4) 7/2 5 /2 4 (4 0 2) 1 3.6 (6) 9

552 5/2 9/2~ (5 1 4) 9» 1 1.1 (6) 10

686 - 1 1.8 (6) 10

10. 84 5/2 5/2+(6 4 2) 3/2 1 /2 -(5 3 0) 1 1.88(6) 11

26 - 7/2 l / 2 - ( 5 3 0) 1 3.1 (4) 11

11. Pa_2a3 87 6/2 5 /2 4 (6 4 2) 3/2 1 /2 -(5 3 0) 1 8.7 (5) 11 29 5/2 5 /2 - (6 4 2) 5/2 1/2 4 (6 3 1) 1 3.8 (4) 11

12. ^{N p 2 3 7} 267 3/2 l/2 + (5 3 0) 5/2 6 /2 - (6 4 2) 1 6.4 (7) 12

13. 57 7/2 7 /2 -(7 5 3) 5/2 1/24(6 3 1) 2 5.5 (8) 13

76 7/2 1/24(6 3 1) 2 8.7 (8) 13

316 ^{, ,} 2 9.4 (8) 14

334 5/2 1/2 4 (6 3 1) 2 8.4 (8) 14

14. 267 6/2 5 /2 + (6 3 2) 3/2 l / 2 - ( 5 2 1) 1 1.5 (5) 16

323 »» 1/2 1/2- (5 2 1) 1 1.5 (5) 16

15. Hfl77 55 23/2 2 3 /2 - ( ?) 21/2 7 /2 4 (4 0 4) 7 6.0 (13) 30

Even Nuclei

1. Eri«8 1016 3 3 - 2 0 4 2 1.1 (10) 18

831 4 0 4 2 3.7 (9) 18

1464 »> 2 0 4 2 1.5 (9) 19

1280 »» 4 0 4 2 1.6 (8) 19

2. Yb'7o 93 8 8 - 8 0 4 7 6.0 (13) 16, 23

3. L u i’^8 200 1 1 - 7 7 4 6 1.1 (16) 20, 22

4. Hfi70 ₈₉ 8 8 - 8 0 4 7 1.0 (13) 17, 23

Systematica of K-isomerism ₆₄₁

Table 1 (contd.) iC-forbiddeu Transitions Even Nuclei

G a in m il- i-ay

SI. N iicJous e n e r g y m I n it ia l S ta le Kinul S ta te V

No. K o V / K n{NNzA) J K 7r(JN^A\A)

5. ybl76 94 8 8 - 8 0 - f 7

G. 57 8 8 - 8 0 - f 7

7. yyaeo 3 9 0 S 8 - 8 0 1* 7

S. VVXB2 1189 2 2 - 0 0 4- 1

1273 3 2 - 2 0 4* 1

1045 4 0 4^{. 1}

9. 552 8 8 8 0 4- 7

10. ptl84 6 1 0 8 8 - 8 0 H- 7

11. 3 5 5 5 5 - - 4 2 h 2

287 99 ^{5 2 I 2}

208 6 2 .

lv-forb id d (*ii JMj T ra n s itio n s

1. T „i167 63 7 /2 7 /2 f-(4 0 4) 5 /2 J/24 (4 1 1) 2

37 7 /2 l / 2 4 - ( l 1 1) 2

.> ₁₇₇ 7 /2 li'l I-(4 0 4) 7 /2 1 /2 4 -(4 1 1) 0

198 7 /2 7 / 2 - K ‘l 0 4) 5 /2 1/2-1 (4 1 1 ) 2

3, Y b ie o 104 5 /2 5 / 2 H-(5 1 2) 3 /2 l/24'(^> ^ 1) J

92 .5/2 1 /2 -I (5 2 1) .>

4. Y b m 122 5 /2 5 / 2 - f ( 5 1 2) 1/2 1 /2 4 -(5 2 1) 1

56 - S /2 l / 2 ^ (5 2 I) 1

5. 917 3 3 + 4 0 1 ²

1004 4 3 { ^{4 0} J- *>

1076 3 3 -f

2

6. ybi73 4 6 5 3 /2 l / 2 + (5 2 1) .5/2 5 /2 1 (5 ] 2) 1 7. Hfi77 _{1 4 .2} 2 3 /2 2 3 /2 ™-(?) 2 1 /2 9 / 2 - { 0 2 4 ) (»

8. 41 7 /2 7 /2 ~ ( 5 0 3) 7 /2 3 / 2 - ( 5 1 2) 1

161 6 /2 3 / 2 - ( 5 1 2) 1

144 9 /2 l / 2 - ( 6 1 0) 2

2 4 6 7 /2 1 / 2 - ( 5 1 0 ) 2

3 5 4 5 /2 1 / 2 - ( 5 1 0) 2

9. 29 3 /2 1 /2 4 -(5 3 0 ) 5 /2 6 /2 ! (5 2 3) 1

10. 2 7 8 5 /2 5 / 2 + ( 6 2 1) 3 /2 1 / 2 4 ( 6 8 >) ¹

228 6 /2 1 / 2 4 ( 6 3 1) I

210 7 /2 1 / 2 4 ( 0 3 1) 1

1 1. Cf251 58.5 7 /2 7 / 2 + ( 6 1 3) 6/2 l/2 + (6 2 0)

2

12. 58.3 7 /2 7 / 2 + ( 6 1 3) 5/2 l/2 + (6 2 0) ²

— .

___ ...

_

i l .F Ref.

6 . 0 (13) 17 2 . 8 (1 6) 23 1 .4 4 (1 2 ) 23 3 . 0 (7 ) 25 3 . 3 (8 ) 26 2 . 5 (8 ) 26 6 . 6 ( 1 1 ) 23 2 .1 3 (1 2 ) 23 1 . 6 ( 8 ) 28 5 1 (8) 28

1 .6 5 (7 ) 28

4 .1 (5) 5 3 (5) 8 .3 (5 ) 6 .6 (5) 1 .3 (1) 7 . 0 (3) (4) 6 . 7 (4) 5 . 0 (6) 7 . 6 (6) 4 . 0 (6)

3 3 3 3 31

31

31 31 21 21 21

7 . 5 (3) 5 6 . 6 (1 0 ) 30 1 .2 (4) 3 . 8 (4) 9 . 6 (4) 4 . 6 (4) 3 . 3 (6 )

24 24 24 24 24 8 . 4 (3) 12 6 . 0 (4) 14 4 . 7 (4) 14 9 .1 (3) 14 3 .4 (4 ) 32 1 . 5 ( 6 ) 16

642

Table 1 (contd.) A'-forbiddon Transitions M . 8. Hajput and M. L. Sekgat

No.SI. Nucleus

Gamma- ray

energy in Initial State

koV J K n{NNzN) Final State

J K n{NNzA)

V H.F. I

1. 109 7/2 7/2 + (4 0 4) 3/2 l/2 + (4 1 1) 1 1.8 (3) 3

2. 308 7/2 7/2+ (4 0 4) 3/2 l/2+ (4 1 1) 1 1.8 (3) 4

3. 917 3 3 4 4 0 + 1 1.8 (3) 17

1095 3 3 4 2 0 4 1 2.9 (3) 17

4. 994 0 6 -f ₆ 0 4- 4 8 .6 (7) 17

1265 0 6 4- 4 0 + 4 7.0 (9) 17

6. HflTO 737 6 6 + ₆ 0 4- 4 4.6 (6) 17

1045 6 6 4 0 + 4 4.8 (6) 17

6. ^{H f l 7 7} 229 23/223/2-( ? ) 19/2 9 /2 -(6 2 4) 5 1 . 0 (8) 30

7. W102 144 7/2 7 /2 -(5 0 3) 5/2 1/2 - (6 1 0) 1 2.5 (2) 24

246 , , 7/2 1 /2 -(5 1 0) 1 1 . 1 (2) 24

354 it 6/2 l /2 - ( 5 1 0) 1 6.9 (2) 24

407 - 3/2 l /2 - ( 6 1 0) 1 4.4 (3) 24

8. 900 6 6 + 4 0 + 4 1 . 0 (1 1) 29

746 6 6 + 6 0 + 4 0 .6 (1 2) 29

540 6 6 + 8 0 + 4 1 . 0 (1 2) 29

Notation ; 4.4(3) moans 4.4 x 10'’

Ref.

From tlio present systematic study of the hindrance factors (H.F.) with the forbiddonnoss number, it is found that in the case of and ilfj transitions, log of hindratJO factor (log H.F.) per- degrejo forbiddonnoss of tho transition decreases, as the degree of forbiddonnoss increases from v = 1 to v = 1. Th(Hjretically, (Bohr and Mottolson 1903), it is not possible to explain such a largo variation in log H.F. por degree forbiddonnoss of tho transition. In tho case of transitions, log of hindrance factor per degree forbiddonnoss of the transitsion deoroasos at a slower rate in comparision with E^ and transitions.

Tlio authors ai’o thankful to Professor Rais Ahmed for his kind interest.

REFERENCES USED IN THE TABLE 1) K, E. G. Lobner and S. A. Do Witt, Physics Letters, 12, 238 (1964).

2) K. E. G. Lonber and 8. A. Do Witt, Physics Letters,

12,

3) T. Tamura, Nuclear Physics, 62, 306, (1965).

4) P Alexander and F. Boehm, Nuclear Physics,

46,

5) T. Kuroyanagi and T. Tamura, Nuclear Physics, 48, 675, Q963).

6) S. Bjorholm et ah. Nuclear Physics, 78, 593, (1966).

7) M. H. Jogerson, O. B. Nielson and O. Skilbried, Nuclear Physics, 84, 609 (1906).

8

) J. D. Newton,

117, 1910, (1960).

9) E. Bashsandy, et ol. Physics, 81, 1125, (1965).

Systematica o f K-isom erism 643

1 0) K. TM. Bisguard et al, Nuclear Phyaics, 71, 192, (1065).

11) F. Asaro

117, 192, (1900).

1 2) J. P. Unik, UCRL-U105, (19HO) ^UnpubliHluMl).

13) M. Vergnes, et al, Nuclear Physics, 39, 310, (1062).

14) S. G. Nilftoa and J. O. Rasmussari, Nuchar 5, 017, (1957).

15) F. Asaro, el al, Phya Rev., 133B, 285, (1904).

16) B. Harniatz, et al, Phya. Rev., 128, 1186 (1902).

17) J. Borggron, et al. Nuclear Phyaics, 96, 581, (1967).

18) J , J. Roidy, et al, Phya. Rev., 133H, 556, (1964).

19) E. Bodens;.odt, et al,

Z.

20) M. A. Preston, “ Physics o f the NucIimih’ * Addisioii-Wesley Pub. Co. London p. 448, (1962;.

21) G. Gunther, et al. Nuclear Physics, 61, 051, ^1905).

22) H. J. Prask, et al. Nuclear Phyaics, 29, 100, (1962).

23) J. Burdue, R. M. Diamond and F. ^{S .} Stefl\‘ns, Nuclear Physics, 85, 483, (1900).

24) V. Honig, et al. Nuclear Physics, 8 6, 057, (1900).

25) M. Dorkins, et al. Nuclear Physics, 61. 33, (1905).

2 0) E. Bashandy, et al, Naclear Physics, 41, 433, (1903).

27) ISiicloar Data shoets, National Academy o f Sciences N.R.C. Washington 25-D.C^

28) S, Bjorholm and S. G. Nison, Nuclear Physics, 30, 448, (1962).

29) S. E. Bandorvosch and P. Day, Nuclear Physics, 80, 488, (1902).

30) E. BodenstedT, et al, Z. Fysik, 190, 00, (1900).

3J) K. E. G. Lobuer, Ph.D. Thesis 1905, Uuiv. o f Amsterdam, (unp^blislied).

32) F. Asaro, c( al, Phys. Rev., 133B, 291, (1904).

R E F E R E N C E S

Biatt, J. M. and Weisskopf, V. F., 1952, Thenrcfical Nuclear Physics, John Wiley and Sons, Now York.

Burdue, J. et al, 1966, Nuelvar P h y s ic s , 85, 483.

Borgreen, J., 1967, Nuclear Physics, 98, 851.

Bohr, A. and Mottelson, B. R ., 1963, A tou iu a iya K uerynja, 15, 41.

Bleumberg, H, et al, 1907, Nuclear Physics, 90, 60.

Curtis Mi(‘hol, F., 1964, Phys. Rev., 133B, 530.

Goldhaber, G. S. and Mc*Ke*owHn, 1967, 7V/;yv. Rer., 158, llOo.

--- 1966, International Conf. on Weak Inter., (3jica«o.

Hager, A, and Seltzer, E., 1960, Physics Letters, 20, 180.

Lawson, R . D. and Segal, R. E., I960, Phys. Rev. Letters. 16, 10 0 0.

Mayor, M. G. and Jonseii, J. H. D., 19‘>2, N>«-lear Shell Slrvcture, John Wiley and Sons Now Y'ork.

Mottelson, B. R. ajid Nilson, S. G., 1959, Mat. Fya. Medde. Skr. Hchhih., 1, 8, 1.

Nathan, O. and Nilson, S. G., 1965, a - f i - y Spectroscopy pt. T. North Hollaad I’ ubl.

Co. Amsterdam, p.636.

Paul, H . et al, 1967, Phys. Rev., 158, 1112.