Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reexamination of the $\beta^+$ decay process of $^{13}\rm{N}$ nucleus   It is known from the scattering theory that the phase-shift of elastic
collision does not provide a unique potential to describe the bound state of
the two-particle system. The bound state wave function is the most crucial
input for various nuclear processes bearing astrophysical significance. In this
paper, we emphasize on the important role of the asymptotic normalization
coefficients for description of the $^{13}\rm{N}\longrightarrow
{^{13}\rm{C}}+\beta^++\nu_e$ reaction. Using experimental data of the elastic
scattering phase-shift of proton and neutron on $^{12}\rm{C}$, we find the
asymptotic normalization coefficients which determine the tail of the bound
state wave functions. This allows us to modify the wave functions of
$^{13}\rm{N}$ and $^{13}\rm{C}$ within the single-particle approach using the
inverse scattering theory. These wave functions are used to determine the
nuclear matrix element for calculation of the half-life and log{\textit ft}
values of $\beta^+$ decay of $^{13}\rm{N}$. The calculated values of the
log{\textit ft} and half-life are smaller than the measured values when the
single-particle wave functions are employed. Using overlap functions, instead
of single-particle functions, we obtain a better comparison. The overlap
function is represented as the product of single-particle function and the
corresponding spectroscopic factor.

33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org