Reaction Rates Calculations in Dense Stellar Matter. Mary Beard University of Notre Dame. [email protected] Frontiers 2005. Aim: To establish a general reaction rate expression for all stellar burning regimes To establish uncertainties in existing reaction rate expressions.
Accreting neutron stars: The ashes of the rp process are compressed and undergo electron captures producing extremely neutron rich, light nuclei
(fusion cross sections)
M. Stoitsov et al., Phys. Rev. C58 (1998) 2086.
A. V. Afanasjev et al., Phys. Rev. C60 (1999) 051303.
Phys. Rev. Lett. 78 (1997) 3270
Phys. Rev. Lett. 79 (1997) 5218
Phys. Rev. C58 (1998) 576
Phys. Rev C66 (2002) 014610
São Paulo potential
The Nuclear Potential
- Densities obtained through theoretical calculations (RMF, for example).
Pycnonuclear Reaction Rates
In a neutron star crust, ions form a Coulomb lattice structure surrounded by a degenerate electron gas.
Electron screening effects become so strong that rates of nuclear reactionsincrease considerably even at low energies;
Pycnonuclear reactions take place under very high density conditions and are more sensitive to density than to temperature – from the Greek, pyknos means compact, dense;
Pycnonuclear reactions between neutron-rich isotopes can provide a new heat source in accreting neutron star crust.
There are a couple of models available for pycnonuclear calculations,
(eg Salpeter and Van Horn Astrophys. J. 155, 183 1969)
All can be written in one general (user-friendly) way, with
dimensionless parameters representing model differences
Where length parameter λ is defined by:
CPYC, Cexp and CL are dimensionless model parameters
Coupled quantum Coulomb system
Strongly coupled quantum system
Coupled classical Coulomb system
Thermonuclear reaction rate is defined by:
Where Pth and Fth are given by
This reduces to appropriate expression in all burning
regimes; when T>>Tp ΔR Rth >> Rpyc retrieve Rth T 0 ΔR 0 retrieve Rpyc
By Analogy, the thermally enhanced pycnonuclear rate can be written as:
Where P and F are given by:
The rates involving isotopes with identical charge number show only minor differences which are entirely due to the difference in S-factor;
For higher Z-values the rates decrease steeply at density values less than 1012 g/cm3 because of the strong Z-dependence in the pycno equation.
Summary show only minor differences which are entirely due to the difference in S-factor;
We are using the São Paulo potential to describe the fusion process.
We are proposing a single analytical expression for the fusion rate, which is valid in all regimes. The parameters reflect theoretical uncertanties of the reaction rates.
An exact calculation should take into account many effects as lattice impurities and imperfections, classical motion of plasma ions, related structure of Coulomb plasma fields, etc.
The next step is extend the treatment presented for one-component-plasma case towards a general formalism for the fusion rate between different isotopes.