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On some negative parity states in 148Sm
PHYSICS
Volume 17, number 3
for their cooperation. They are indebted to Dr. K. Matsuda for providing the target of 90Er. They are much indebted to the members of the INS DWBA project for making available the INS DWBA-1 code. References
1. K. W. Ford, Phye. Rev. 98 (1955) 1516. 2. B.F.Bayman, A.S.Reiner andR.K.Sheline, Phye. Rev.115 (1959) 1627. 3. I.Talmi and I.Unna, Nuclear Phys. 19 (1960) 225.
ON SOME
NEGATIVE
15 July 1965
LETTERS
4. V.K.Tha&appan. Y.R.WaghmareandS.P.Pandya, Proar. Theoret. Phve. 26 (1961) 22. 5. B.LyCohen and A.G.Ruh& Phys.Rev.lll (1958) 1568. 6. W. T. Pink&on and G. R. Satchler, Nuclear Phys. 27 (1961) 270. H.Ogata, S.Tomita, M.InoueandY. 7. L&&he, 6kuma. Phvaics Letters (to be published). 8. S.Ran&at&am, Phys.Rev.135 (1964) Bi288. 9. D.L.Hendrie and G. W. Farwell, Physics Letters 9 (1964) 321. 10. R.B.Day, A.G.Blair and D.D.Armstrong, Physics Letters 9 (1964) 327.
PARITY
STATES
IN 143Sm
K. H. BHATT Physical Research Laboratwy Navrangpura, Ahmedabad-9, India
Received 10 June 1965
Some of the low-lying states in 148Sm observed by Baba et ai.[I] are shown in fig. la. Following the usual custom, the first 2+ might be regarded as a single quadrupole phonon state and the first 3- as a single octupole phonon state. The quartet of levels l-, 5-, 3- and 4- is centered around an energy which is very close to the sum of the energies of the first 2+ and 3states. This suggests that these states might be due to the simultaneous excitation of a quadrupole and an octupole phonon. Such a double excitation would give rise to five states l-, 2-, 3-, 4- and 5-. Hence if we wish to attribute the negative parity states to the coupling of the quadrupole to the octupole phonon, it is essential that the 2- be experimentally observed. The wave functions of the quadru-octupole quintet may be written as: ICI->= ([2+, 3-1 J-j
) J = 1, 2, 3, 4, 5.
6 -1-91
--a.03
,----I.90
4-3--
----
3P-1.73 5--1.60 l------l.46
4+---+1e
1’92 I.86 _-_-___-1.71
2--i-63 5--l~58
--
1.39
3--1.16
a+-
0.55
(1)
where the bracket [2+, 3-l indicates vector coupling of the angular momenta 2 and 3 to give the resultant J. The energy splitting of these states (eq. 1) will be determined by the residual interaction between the two collective modes of the nucleus. The sequence l-, 5-, 3-, 4- suggests that the residual interaction contains a large “quadrupole” compo282
4
o-
A)
EXPERlMENTnL
8) CALCULATED
Fig. 1. Some energy levels in 1488,. The positive and negative parity states are drawn separately for the sake of clarity.
Volume 17, number 3
PHYSICS
nent. Assuming a quadrupole-quadrupole interaction between the two collective modes the energy splittings of the negative parity states are given by: AEJ = -CW
(J 2 3 2; 3 Z),
(2)
where W is Racah coefficient and C is a constant which determines the strength of the interaction. The spectrum of negative parity states, obtained by using eq. (2) is shown in fig. lb. The value of the constant Cused is C = 2.25 MeV. The energy at which the dashed line is drawn corresponds to the sum of the energies of the first 2+ and 3’ states respectively. The agreement of the calculated spectrum with the experimental one is adequate. The purpose of this simple calculation of the energies was just to add to the plausibility of the present interpretation of these negative parity states and to get some idea about the location of the missing 2- state. It would be of interest to look for such a 2- close to the 5- state. If these negative parity states indeed arise due to the quadrupole-octupole phonon coupling, their y-decay should exhibit interesting selection rules such as: (a) The transition l- --) O+ should be hindered appreciably compared to the single particle estimates, since it involves a double deexcitation of the nucleus. This is indeed obseryed by Metzger
PI*
(b) The transition from any member IJ-> of the quadrn-octupole multiplet to the quadrupole ]2+) state would occur through the collapse of the octupole phonon. Hence the y-rays corresponding to these transitions should contain an appreciable E3 component. The reduced E3 transition proba-
LETTERS
15 July 1965
bility B(E3) would be given by: B(E3, J- 4 2+) =B(E3,
3- - O+).
(3)
To be specific, the transition l- or 3- (1836 keV) + 2+ should have highly hindered El and appreciable E3 components compared to single particle estimates. Metzger [Z] has measured the value of B (El, l- --) 2+ and indeed finds it reduced by a factor of lo- d compared to single particle estimates. (c) The transition from the IJ-) multiplet (eq. 1) to the octupole 13’) state would occur with the collapse of the quadrupole phonon and we would expect that B(E2, J- -3-
(octupole)) = B(E2, 2+ -, O+). (4)
(d) If the 4+ state at 1181 keV can be regarded as a “two quadrupole phonon” state the reduced transition probability B(E1) for the decay I[Z+, 3-l 5-) - I[Z+, 2’1 4+) would be given by B(E1, 5- -
4+) = B(E1, 3- -
2+).
(5)
It would be of interest to study these various r-decays and check the relations given in eqs. (3) (4) and (5). It is likely that similar negative parity multiplets might be seen in other even mass nuclei near to 148Sm. I would like to thank Prof. S. P. Pandya for discussion and for reading the manuscript.
References 1. C.V.K.Baba. G.T.EwanandJ.F.Suarez. Nuclear Physics 43 (1963) 264 and Nuclear Physics 43 (1963) 285. 2. F. R.Metzger, Phys. Rev. 137 (1965) B1415.
*****
ON THE
VIOLATION OF GALLAGHER AND MOSZKOWSKI’S COUPLING RULES IN 166Ho G. L. STRUBLE and J. 0. RASMUSSEN Radiation Laboratory, University of California,
Lawrence
Berkeley,
California
Received 12 June 1965 Recently several publications [l-3] have appeared which attempt to justify theoretically the validity of the empirical coupling rules of Gal-
lagher and Moszkowski [4] for deformed odd-odd nuclei. These rules state that the lower energy band of the two possible rotational bands formed 283
Volume 17, number 3
for their cooperation. They are indebted to Dr. K. Matsuda for providing the target of 90Er. They are much indebted to the members of the INS DWBA project for making available the INS DWBA-1 code. References
1. K. W. Ford, Phye. Rev. 98 (1955) 1516. 2. B.F.Bayman, A.S.Reiner andR.K.Sheline, Phye. Rev.115 (1959) 1627. 3. I.Talmi and I.Unna, Nuclear Phys. 19 (1960) 225.
ON SOME
NEGATIVE
15 July 1965
LETTERS
4. V.K.Tha&appan. Y.R.WaghmareandS.P.Pandya, Proar. Theoret. Phve. 26 (1961) 22. 5. B.LyCohen and A.G.Ruh& Phys.Rev.lll (1958) 1568. 6. W. T. Pink&on and G. R. Satchler, Nuclear Phys. 27 (1961) 270. H.Ogata, S.Tomita, M.InoueandY. 7. L&&he, 6kuma. Phvaics Letters (to be published). 8. S.Ran&at&am, Phys.Rev.135 (1964) Bi288. 9. D.L.Hendrie and G. W. Farwell, Physics Letters 9 (1964) 321. 10. R.B.Day, A.G.Blair and D.D.Armstrong, Physics Letters 9 (1964) 327.
PARITY
STATES
IN 143Sm
K. H. BHATT Physical Research Laboratwy Navrangpura, Ahmedabad-9, India
Received 10 June 1965
Some of the low-lying states in 148Sm observed by Baba et ai.[I] are shown in fig. la. Following the usual custom, the first 2+ might be regarded as a single quadrupole phonon state and the first 3- as a single octupole phonon state. The quartet of levels l-, 5-, 3- and 4- is centered around an energy which is very close to the sum of the energies of the first 2+ and 3states. This suggests that these states might be due to the simultaneous excitation of a quadrupole and an octupole phonon. Such a double excitation would give rise to five states l-, 2-, 3-, 4- and 5-. Hence if we wish to attribute the negative parity states to the coupling of the quadrupole to the octupole phonon, it is essential that the 2- be experimentally observed. The wave functions of the quadru-octupole quintet may be written as: ICI->= ([2+, 3-1 J-j
) J = 1, 2, 3, 4, 5.
6 -1-91
--a.03
,----I.90
4-3--
----
3P-1.73 5--1.60 l------l.46
4+---+1e
1’92 I.86 _-_-___-1.71
2--i-63 5--l~58
--
1.39
3--1.16
a+-
0.55
(1)
where the bracket [2+, 3-l indicates vector coupling of the angular momenta 2 and 3 to give the resultant J. The energy splitting of these states (eq. 1) will be determined by the residual interaction between the two collective modes of the nucleus. The sequence l-, 5-, 3-, 4- suggests that the residual interaction contains a large “quadrupole” compo282
4
o-
A)
EXPERlMENTnL
8) CALCULATED
Fig. 1. Some energy levels in 1488,. The positive and negative parity states are drawn separately for the sake of clarity.
Volume 17, number 3
PHYSICS
nent. Assuming a quadrupole-quadrupole interaction between the two collective modes the energy splittings of the negative parity states are given by: AEJ = -CW
(J 2 3 2; 3 Z),
(2)
where W is Racah coefficient and C is a constant which determines the strength of the interaction. The spectrum of negative parity states, obtained by using eq. (2) is shown in fig. lb. The value of the constant Cused is C = 2.25 MeV. The energy at which the dashed line is drawn corresponds to the sum of the energies of the first 2+ and 3’ states respectively. The agreement of the calculated spectrum with the experimental one is adequate. The purpose of this simple calculation of the energies was just to add to the plausibility of the present interpretation of these negative parity states and to get some idea about the location of the missing 2- state. It would be of interest to look for such a 2- close to the 5- state. If these negative parity states indeed arise due to the quadrupole-octupole phonon coupling, their y-decay should exhibit interesting selection rules such as: (a) The transition l- --) O+ should be hindered appreciably compared to the single particle estimates, since it involves a double deexcitation of the nucleus. This is indeed obseryed by Metzger
PI*
(b) The transition from any member IJ-> of the quadrn-octupole multiplet to the quadrupole ]2+) state would occur through the collapse of the octupole phonon. Hence the y-rays corresponding to these transitions should contain an appreciable E3 component. The reduced E3 transition proba-
LETTERS
15 July 1965
bility B(E3) would be given by: B(E3, J- 4 2+) =B(E3,
3- - O+).
(3)
To be specific, the transition l- or 3- (1836 keV) + 2+ should have highly hindered El and appreciable E3 components compared to single particle estimates. Metzger [Z] has measured the value of B (El, l- --) 2+ and indeed finds it reduced by a factor of lo- d compared to single particle estimates. (c) The transition from the IJ-) multiplet (eq. 1) to the octupole 13’) state would occur with the collapse of the quadrupole phonon and we would expect that B(E2, J- -3-
(octupole)) = B(E2, 2+ -, O+). (4)
(d) If the 4+ state at 1181 keV can be regarded as a “two quadrupole phonon” state the reduced transition probability B(E1) for the decay I[Z+, 3-l 5-) - I[Z+, 2’1 4+) would be given by B(E1, 5- -
4+) = B(E1, 3- -
2+).
(5)
It would be of interest to study these various r-decays and check the relations given in eqs. (3) (4) and (5). It is likely that similar negative parity multiplets might be seen in other even mass nuclei near to 148Sm. I would like to thank Prof. S. P. Pandya for discussion and for reading the manuscript.
References 1. C.V.K.Baba. G.T.EwanandJ.F.Suarez. Nuclear Physics 43 (1963) 264 and Nuclear Physics 43 (1963) 285. 2. F. R.Metzger, Phys. Rev. 137 (1965) B1415.
*****
ON THE
VIOLATION OF GALLAGHER AND MOSZKOWSKI’S COUPLING RULES IN 166Ho G. L. STRUBLE and J. 0. RASMUSSEN Radiation Laboratory, University of California,
Lawrence
Berkeley,
California
Received 12 June 1965 Recently several publications [l-3] have appeared which attempt to justify theoretically the validity of the empirical coupling rules of Gal-
lagher and Moszkowski [4] for deformed odd-odd nuclei. These rules state that the lower energy band of the two possible rotational bands formed 283