263 research outputs found
Connection between effective-range expansion and nuclear vertex constant or asymptotic normalization coefficient
Explicit relations between the effective-range expansion and the nuclear
vertex constant or asymptotic normalization coefficient (ANC) for the virtual
decay are derived for an arbitrary orbital momentum together with
the corresponding location condition for the () bound-state energy. They
are valid both for the charged case and for the neutral case. Combining these
relations with the standard effective-range function up to order six makes it
possible to reduce to two the number of free effective-range parameters if an
ANC value is known from experiment. Values for the scattering length, effective
range, and form parameter are determined in this way for the O+,
and He collisions in partial waves where a bound state
exists by using available ANCs deduced from experiments. The resulting
effective-range expansions for these collisions are valid up to energies larger
5 MeV.Comment: 17 pages, 6 figure
Influence of low energy scattering on loosely bound states
Compact algebraic equations are derived, which connect the binding energy and
the asymptotic normalization constant (ANC) of a subthreshold bound state with
the effective-range expansion of the corresponding partial wave. These
relations are established for positively-charged and neutral particles, using
the analytic continuation of the scattering (S) matrix in the complex
wave-number plane. Their accuracy is checked on simple local potential models
for the 16O+n, 16O+p and 12C+alpha nuclear systems, with exotic nuclei and
nuclear astrophysics applications in mind
Coulomb renormalization and ratio of proton and neutron asymptotic normalization coefficients for mirror nuclei
Asymptotic normalization coefficients (ANCs) are fundamental nuclear
constants playing important role in nuclear reactions, nuclear structure and
nuclear astrophysics. In this paper the physical reasons of the Coulomb
renormalization of the ANC are addressed. Using Pinkston-Satchler equation the
ratio for the proton and neutron ANCs of mirror nuclei is obtained in terms of
the Wronskians from the radial overlap functions and regular solutions of the
two-body Schr\"odinger equation with the short-range interaction excluded. This
ratio allows one to use microscopic overlap functions for mirror nuclei in the
internal region, where they are the most accurate, to correctly predict the
ratio of the ANCs for mirror nuclei, which determine the amplitudes of the
tails of the overlap functions. Calculations presented for different nuclei
demonstrate the Coulomb renormalization effects and independence of the ratio
of the nucleon ANCs for mirror nuclei on the channel radius. This ratio is
valid both for bound states and resonances. One of the goals of this paper is
to draw attention on the possibility to use the Coulomb renormalized ANCs
rather than the standard ones especially when the standard ANCs are too large.Comment: 20 pages, 14 figure
Combined method to extract spectroscopic information
Spectroscopic factors (SF) play an important role in nuclear physics and
astrophysics. The traditional method of extracting SF from direct transfer
reactions suffers from serious ambiguities. We discuss a modified method which
is based on including the asymptotic normalization coefficient (ANC) of the
overlap functions into the transfer analysis. In the modified method the
contribution of the external part of the reaction amplitude, typically
dominant, is fixed and the SF is determined from fitting the internal part. We
illustrate the modified method with reactions on , and targets at different energies. The
modified method allows one to extract the SF, which do not depend on the shape
of the single-particle nucleon-target interaction, and has the potential of
improving the reliability and accuracy of the structure information. This is
specially important for nuclei on dripline, where not much is known.Comment: accepted in Phys. Rev. C, 4 pages and 2 figure
Clarification of the relationship between bound and scattering states in quantum mechanics: Application to 12C + alpha
Using phase-equivalent supersymmetric partner potentials, a general result
from the inverse problem in quantum scattering theory is illustrated, i.e.,
that bound-state properties cannot be extracted from the phase shifts of a
single partial wave, as a matter of principle. In particular, recent R-matrix
analyses of the 12C + alpha system, extracting the asymptotic normalization
constant of the 2+ subthreshold state, C12, from the l=2 elastic-scattering
phase shifts and bound-state energy, are shown to be unreliable. In contrast,
this important constant in nuclear astrophysics can be deduced from the
simultaneous analysis of the l=0, 2, 4, 6 partial waves in a simplified
potential model. A new supersymmetric inversion potential and existing models
give C12=144500+-8500 fm-1/2.Comment: Expanded version (50% larger); three errors corrected (conversion of
published reduced widths to ANCs); nine references added, one remove
Quantum Monte Carlo calculations of spectroscopic overlaps in nuclei
We present Green's function Monte Carlo calculations of spectroscopic
overlaps for nuclei. The realistic Argonne v18 two-nucleon and
Illinois-7 three-nucleon interactions are used to generate the nuclear states.
The overlap matrix elements are extrapolated from mixed estimates between
variational Monte Carlo and Green's function Monte Carlo wave functions. The
overlap functions are used to obtain spectroscopic factors and asymptotic
normalization coefficients, and they can serve as an input for low-energy
reaction calculations
Astrophysical factor for the reaction from -matrix analysis and asymptotic normalization coefficient for . Is any fit acceptable?
The reaction provides a path from the CN
cycle to the CNO bi-cycle and CNO tri-cycle. The measured astrophysical factor
for this reaction is dominated by resonant capture through two strong
resonances at and 962 keV and direct capture to
the ground state. Recently, a new measurement of the astrophysical factor for
the reaction has been published [P. J.
LeBlanc {\it et al.}, Phys. Rev. {\bf C 82}, 055804 (2010)]. The analysis has
been done using the -matrix approach with unconstrained variation of all
parameters including the asymptotic normalization coefficient (ANC). The best
fit has been obtained for the square of the ANC fm,
which exceeds the previously measured value by a factor of . Here we
present a new -matrix analysis of the Notre Dame-LUNA data with the fixed
within the experimental uncertainties square of the ANC
fm. Rather than varying the ANC we add the contribution from a
background resonance that effectively takes into account contributions from
higher levels. Altogether we present 8 fits, five unconstrained and three
constrained. In all the fits the ANC is fixed at the previously determined
experimental value fm. For the unconstrained fit with
the boundary condition , where is the energy of the
second level, we get keVb and normalized , i.e. the result which is similar to [P. J. LeBlanc {\it et
al.}, Phys. Rev. {\bf C 82}, 055804 (2010)]. From all our fits we get the range
keVb which overlaps with the result of [P. J.
LeBlanc {\it et al.}, Phys. Rev. {\bf C 82}, 055804 (2010)]. We address also
physical interpretation of the fitting parameters.Comment: Submitted to PR
Generalized Faddeev equations in the AGS form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction
Theoretical description of reactions in general, and the theory for
reactions, in particular, needs to advance into the new century. Here deuteron
stripping processes off a target nucleus consisting of nucleons are
treated within the framework of the few-body integral equations theory. The
generalized Faddeev equations in the AGS form, which take into account the
target excitations, with realistic optical potentials provide the most advanced
and complete description of the deuteron stripping. The main problem in
practical application of such equations is the screening of the Coulomb
potential, which works only for light nuclei. In this paper we present a new
formulation of the Faddeev equations in the AGS form taking into account the
target excitations with explicit inclusion of the Coulomb interaction. By
projecting the -body operators onto target states, matrix three-body
integral equations are derived which allow for the incorporation of the excited
states of the target nucleons. Using the explicit equations for the partial
Coulomb scattering wave functions in the momentum space we present the AGS
equations in the Coulomb distorted wave representation without screening
procedure. We also use the explicit expression for the off-shell two-body
Coulomb scattering -matrix which is needed to calculate the effective
potentials in the AGS equations. The integrals containing the off-shell Coulomb
T-matrix are regularized to make the obtained equations suitable for
calculations. For and nucleon-target nuclear interactions we assume the
separable potentials what significantly simplifies solution of the AGS
equations.Comment: 34 pages, 13 figure
{Once more about astrophysical factor for the reaction
Recently to study the radiative capture process a new measurement of the
dissociation in the field of has been reported in [F.
Hammache {\it et al.} Phys. Rev , 065803 (2010)]. However, the
dominance of the nuclear breakup over the Coulomb one prevented from obtaining
the information about the process from
the breakup data. The astrophysical factor has been calculated
within the two-body potential model with potentials determined from
the fits to the elastic scattering phase shifts. However, the
scattering phase shift itself doesn't provide a unique bound state
potential, which is the most crucial input when calculating the
astrophysical factor at astrophysical energies. In this work we emphasize an
important role of the asymptotic normalization coefficient (ANC) for
, which controls the overall normalization of
the peripheral process and is
determined by the adopted bound state potential. We demonstrate that
the ANC previously determined from the elastic scattering -wave
phase shift in [Blokhintsev {\it et. al} Phys. Rev. {\bf C 48}, 2390 (1993)]
gives , which is at low energies about 38% lower than the one
reported in [F. Hammache {\it et al.} Phys. Rev , 065803 (2010)].
We recalculate also the reaction rates, which are also lower than those
obtained in [F. Hammache {\it et al.} Phys. Rev , 065803 (2010)].Comment: 6 pages and 2 figure
Relation between widths of proton resonances and neutron asymptotic normalization coefficients in mirror states of light nuclei in a microscopic cluster model
It has been suggested recently ({\it Phys. Rev. Lett.} 91, 232501 (2003))
that the widths of narrow proton resonances are related to neutron Asymptotic
Normalization Coefficients (ANCs) of their bound mirror analogs because of
charge symmetry of nucleon-nucleon interactions.
This relation is approximated by a simple analytical formula which involves
proton resonance energies, neutron separation energies, charges of residual
nuclei and the range of their strong interaction with the last nucleon. In the
present paper, we perform microscopic-cluster model calculations for the ratio
of proton widths to neutron ANCs squared in mirror states for several light
nuclei. We compare them to predictions of the analytical formula and to
estimates made within a single-particle potential model. A knowledge of this
ratio can be used to predict unknown proton widths for very narrow low-lying
resonances in the neutron-deficient region of the - and -shells, which
is important for understanding the nucleosynthesis in the -process.Comment: 13 pages, 5 figures, submitted to PR
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