Systematic study on fine structure of alpha decay of some odd-even nuclei in
trans-actinide region
338
Proceedings of the DAE-BRNS Symp. on 1Nucl. Phys. 61 (2016)
2*
G. M. Carmel Vigila Bai , R. Nithya Agnes
1. Rani Anna Government College for women, Tirunelveli - 08, Tamil Nadu, India. 2. St. John’s College,
Palayamkottai - 02, Tamil Nadu, India.
Introduction: The unstable nuclei can decay to stable nuclei via the emission of helium nuclei in alpha decay. The
alpha decay theory was formulated by Gamow and independently by Gurney and Condon on the basis of quantum
tunnelling. The fine structure of alpha decay was formulated by Salomon Rosenblum [1] in 1929. In this paper we
have studied the fine structure of alpha decay for odd-even nuclei of Am231-241, Bk235-253, Es243-257 and Md245-261 isotopes
using Cubic plus Yukawa plus Exponential Model [2] by including both quadrupole and hexadecapole deformations
and the spin- parity effects.
Cubic plus Yukawa plus Exponential Model (CYEM): In this work, the spin and the parity of parent and daughter
nuclei are included, with the daughter nucleus having a quadrupole deformation and keeping the cluster spherical. If
the parent nuclei have deformations say quadrupole and hexadecapole and if the Q-value of the reaction is taken as the
origin, the potential for the post - scission region is given by
V(r) = Vc(r) + Vn(r) +ℓ (ℓ+1) ћ2/2µr2 - Vdf (r) – Q
(1)
Here Vc is the coulomb potential between a spheroid daughter and spherical emitted cluster. V n is the nuclear
interaction energy due to finite range effects of Krappe et al; and V df is the change in nuclear interaction energy due to
quadruple and hexadecapole deformations in the daughter nuclei, ‘ℓ’ is the angular momentum carried by the alpha
particle, and ‘µ’ is the reduced mass . The values of natural angular momentum have been obtained from the usual
nuclear spin and parity conservation laws.
The energy of alpha particle emitted from nucleus in alpha decay is
Q = Qg.s→g.s- Ei*
(2)
*
th
Where Ei is the excitation energy of daughter nucleus to the i state. The ground state to ground state Q-value is given
by
𝜀
𝜀
𝜀
Qg.s→g.s =∆𝑀𝑝 − ∆𝑀𝑑 + ∆𝑀𝛼 + [𝑘1 𝑍𝑝 1 − 𝑍𝑑1 − 𝑘2 𝑍𝑐 2 ]
Where Mp, Md, Mα are the mass excess of parent, daughter and alpha nuclei as tabulated by Audi et al [3]. The
quantity k𝑍 𝜀 represents the total binding energy of the Z-electrons in the atom, where k1=8.7x10-6M eV, and 𝜀1 =
2.517 for nuclei of Z ≥ 60 and k2 =13.6 x10-6 M e V and 𝜀2 =2.408 for Z < 60.
Expressing the energies in MeV, lengths in fm and time in seconds for calculating the life time of the decay
system we use the formula,
T=
1.433 × 10 −21
𝐸𝑣
1 + exp(𝑘)
(3)
Results and discussions: We have calculated alpha decay half-lives of odd-even nuclei from ground state of the
parent nucleus to ground and excited states of the daughter nucleus by including quadrupole(𝛽2 ) and hexadecapole
(𝛽4 )deformations of parent and daughter nuclei which are taken from the tables of Moller et al [4] and spin-parity
effects. The calculated half-lives are compared with available data and are found to be good agreement with each
other.The standard deviation is estimated using the following expression.
𝛔=
1
(n − 1)
n
exp . 2
]
[log Titheor . – log Ti
i=1
The estimated standard deviation of the half lives by our model for the ground state to ground state transition is 0.9395
and by ref.[6] is1.250, while the same calculated for the higher excited states is 1.263. The hindrance Factor (HF) is
𝒆𝒙𝒑.
calculated by the formula, HF=
𝑻𝟏/𝟐
𝑻𝒕𝒉𝒆𝒓𝒐.
𝟏/𝟐
. The branching ratio of alpha decay to each state of the daughter nucleus have
been evaluated as
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Bi=
𝜞 𝑸𝒊 ,𝒍𝒊
𝒏 𝑸𝒏 ,𝒍𝒏
× 𝟏𝟎𝟎%
Where the sum n is going over all states, which can be populated during the alpha transition from the ground state of
the parent nucleus.From figure, it is found that the transitions from ground to ground state have the highest branching
ratio value. While going to the higher excited states the branching ratio value is found to be decreased with the
Proceedings
the DAE-BRNS
on Nucl.
Phys.
61 (2016)
339
increase of
hindranceoffactor
value. HenceSymp.
the decay
to those
excited
states of the daughter nuclei are hindered.
Table1: Logarithmic half-lives for alpha decay of odd-even isotopes of some trans-actinide nuclei from ground
state to ground state transitions.
Log T(s)
Decay mode
ℓmin
Q(MeV)
Our model Ref.[5]
Ref.[6]
Expt.[7]
235
Am→231Np+α
1
6.618
5.35
5.78
7.09
5.17
241
237
Am→ Np+α
1
5.680
10.12
10.49
12.02
10.13
243
Am→239Np+α
1
5.481
11.36
11.88
13.18
11.37
247
Bk→243Am+ α
2
5.934
10.08
11.79
9.94
10.64
249
Bk→245Am+ α
2
5.568
12.22
13.67
12.10
13.61
245
Es→241Bk+α
3
7.960
2.53
4.49
3.73
1.82
253
Es→249Bk+α
0
6.784
6.39
6.87
6.65
6.25
249
245
Md→ Es+α
2
8.482
1.19
1.83
0.80
1.34
255
251
Md→ Es+α
2
7.952
3.17
2.70
2.81
3.21
Md→ Es+α
0
7.604
4.14
3.58
5.99
4.30
253
247
80
40
Am
50
30
Branching Ratio cal.%
Branching Ratio cal.
70
60
50
40
30
20
10
0
Md
30
20
10
0
-10
0
-10
7/2- -->7/2+ 7/2- -->9/2+ 7/2- -->11/2+ 7/2- -->5/2-
5/2- -->5/2+ 5/2- -->7/2+
7/2+---->7/2+
7/2+---->9/2+
247
10
1.4
Es
8
241
Am
2.2
2
Hindrance Factor cal.
Hindrance Factor cal.
4
0.8
0.6
0.4
7/2+---->9/2+
Md
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.2
0.4
0.2
0.0
0
257
2.0
1.0
6
7/2+---->7/2+
7/2- -->7/2-
5/2- -->5/2- 5/2- -->9/2+ 5/2- -->7/2-
7/2+---->11/2+
1.2
Hindrance Factor cal.
257
40
20
10
-10
241
Es
Branching Ratio cal.%
257
0.0
7/2+---->11/2+
7/2- -->7/2+ 7/2- -->9/2+ 7/2- -->11/2+ 7/2- -->5/2-
7/2- -->7/2-
-0.2
5/2- -->5/2+ 5/2- -->7/2+ 5/2- -->5/2- 5/2- -->9/2+ 5/2- -->7/2-
Fig.1. Histogram for hindrance factor and branching ratio of Es247 ,
Am241 and Md
257
nuclei.
References:
1.Salomon Rosenblum ,C.R.Acad.Sci.Paris 188 (1929)1401.
2.G.Shanmugam, G.M.CarmelVigilaBai and B.Kamalaharan, Phys. RevC51,2616(1995).
3.M. Wang, G. Audi, A.H. Wapstra, F.G. Kondev, M. MacCormick, X. Xu1, and B. Pfeiffer. The AME2012 atomic
mass evaluation
4.P. Möller , A.J. Sierk , T. Ichikawa , H. Sagawa Nuclear ground-state masses and deformations: FRDM(2012)
5.P. M¨oller, J. R. Nix, and K.-L. Kratz, Atomic Data Nucl. Data Tables 66 (1997).
6.V. Yu Denisov and A A Khudenko, Phys. Rev.C80(2009)034603.
Available online at www.sympnp.org/proceedings
7.http://www.nndc.bnl.gov.