b-Decay Rates of Nuclei in Ground and Excited States
and Effects on the r-Process of Nucleosynthesis
b-Decay rates of excited-state nuclei are calculated using a single-particle model, which incorporates shell energies of
individual nucleons into the mass formula. Energies of two-particle levels are calculated by assuming a Fermi gas model with
shell and pairing forces. A comparison of level energies to those of the spherical shell model for nuclei of the same mass
yields a determination of a configuration mixture of spherical shell model eigenstates characterized by their quantum
numbers. Therefore, the order of the decay is specified. The resulting density of particle states is inserted into the gross
theory of b-decay, so the ease of calculation is maintained with the decay form factors. This model is quite useful in that bdecays of excited state nuclei, which are created by the promotion of nucleons to levels above the Fermi surface, can be
calculated with the same method. The ultimate purpose of this calculation is to determine the effects of b-decays on the rprocess of nucleosynthesis. Since r-process progenitor nuclei are very neutron rich, decay rates must be calculated, and
current models have utilized only ground-state nuclear decay rates. The possibility of a faster progression along the r-process
path, as well as the possible elimination of closed-shells in a small population of the N=82 nuclei due to excitations above the
shell may create an r-process simulation in which the mass 195 nuclei are produced in greater abundance by the time the rprocess freezes out. An r-process model which evolves average b-decay rates as a function of temperature is used. The
environmental parameters of this model simulate those of the supernova hot-bubble region, a strong candidate for the rprocess site. The final freezeout abundance distribution is compared with that of the solar system r-process abundance
distribution.
R.N.
1,2
Boyd ,
r-Process Results
Nearly four decades have
passed since the r-process was
postulated. The nature of the
distribution of heavy elements
in the solar system (left) lead to
the theory that these elements
were produced via neutron
captures on seed nuclei,
producing the r-process path
through very neutron-rich
nuclei (right). A comparison of
the distribution of r-process
elements in the solar system to
that of the metal-poor halo stars
(below-right) indicates that the
r-process is both primary and
unique. An r-process site that
has met nominal success is the
supernova hot-bubble region
(left) above a nascent neutron
star. Difficulties in current rprocess calculations include
their ability to successfully
produce the A~195 peak in the
solar distribution (above-left).
[Cowan et al. (1990)]
dN1
M  (E)  
D ( E ,  )
W ( E ,  ) d
o (E )
d
mc
 3 7
2 
0
1
dN1
Qo D ( E ) d W ( E,  ) f ( E )ddE
Average Decay Rates vs. Temperature
dN
  ni    i 
d
i
W  i ,  k   nk  i   k   NP  me 
 w i; n, l , j 
2
1
n ,l , j
• Each level is a sum of shell model Eigenstates with
coefficient w(i;n,l,j).
• Two-particle levels. Excited states achieved by calculating
levels above the Fermi surface.
• Transition probability function - Can the specified
transition take place, and with what strength?
• Transition Matrix Elements – Takes state availability into
account.
• Nuclei at T0
– Not necessarily in the ground state.
– Distribution of nuclei in excited states:
• Stellar environments
• r-Process effects
– Increased b-decay rates
– Change in many reaction Q-values?
 i   w i; n, l , j n ,l , j
n ,l , j
D E ,    D  f ,  i    w i;  w  f ;     ,  
 ,
100
10
1
Pd-128
M  E   M   i   k  
2
 
i ,k , ,
Sn-135
La-164
Te-150
Pr-171
Tm-195
0.1
2
0
ni nkw i;  w k ;  


   ,  g 

1
2
3
4
5
6
7
8
9
10
Temperature (Billion Kelvin)
Accuracy of Calculated Decay Rates (Ground State)
3
Energetically Possible Decays
Single-Particle States in the Gross
Theory
Neutrons
Protons
(Ln 0.5, Ye =0.4)
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
s-Process Peak
r-Process Peak
[Schramm (1982)]
1.E-08
Excited State Decays
1.E-09
80
140
160
180
200
220
Conclusions
[Sneden et al. (1996)]
Effects of excited state b-decays on the r-process
– Relaxes some constraints
– No artificial adjustments to parameters (e.g.,
entropy) needed
– “Fine Tuning” of the r-process distribution via
b-delayed neutron emission and freezeout
interactions
Future Work
– Improvement of decay rate calculations
– Experiment in progress
• Type II Supernova Model in the Schwarzchild Geometry
• Full Network Calculation (Kajino et al. 1999)
–~3700 Nuclei from A=1-240 from b-Stability to the
Neutron Drip Line
–Extensive network continuous between a-process and rprocess
• Simulation Until Well Beyond Freezeout
• b-Decays Given as Functions of Temperature
References
Kondoh, T., Tachibana, T., Yamada, M., Prog. Theor.
Phys. 72, 708 (1985).
Nakata, H., Tachibana, T., Yamada, M., Nuc. Phys. A
625, 521 (1997).
Otsuki, K., Tagoshi, H., Kajino, T., Wanajo, S., ApJ
533, 424 (2000).
Schramm, D.N., in Essays in Nuclear Astrophysics, ed.
Barnes, C.A., Clayton, D.D., Schramm, D.N.,
(Cambridge Univ. Press), p. 325 (1982).
Sneeden, C., McWilliam, A., Preston, G.W., Cowan,
J.J., Burris, D.L., Armosky, B.J., ApJ 467, 819 (1996).
Tachibana, T., Yamada, M., Yoshida, Y., Prog. Theor.
Phys. 84, 641 (1990).
2
Q

1
1Department
0
-1
-2
[Otsuki et al. (2000)]
Z
120
Solar
A
Even-Even Odd-Z Odd-N Odd-Odd
N
100
Ground State Decays
The Network Calculation
1000
Average Decay Rate (1/s)
5 4
LOG(Calc. Rate/Exp. Rate)
• Continuous distribution of nuclear states
• Fermi and Gamow-Teller transitions (and thus, the
transition matrix elements) are continuous functions of
transition energy
• Decay rates are products of:
– Transition probability
– Nucleons available for decay in parent state
– Availability of states for available nucleons to decay to
– Fermi function
1
2
r-Process Results
The r-Process
b-Decays, Excited States, and the
r-Process
The Gross Theory of b-Decay
and T.
3-5
Kajino
Abundance
M.A.
1
Famiano ,
-3
0.0001
0.001
0.01
0.1
Experimental Rate (1/s)
1
10
100
of Physics, Ohio State University, Smith Lab, 174 West
18th Avenue, Columbus, OH 43210; famiano@mps.ohio-state.edu;
boyd@mps.ohio-state.edu
2Department of Astronomy, Ohio State University, McPherson
Laboratory, 140 West 18th Avenue, Columbus, OH 43210-1173
3National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan; kajino@nao.ac.jp
4Department of Astronomy, University of Tokyo, 7-3-1 Hongo, Bunkyoku, Tokyo 113-0033, Japan
5Department of Astonomical Science, Graduate University for
Advanced Studies, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan