arXiv subjects

Yu. V. Orlov

Publications and source records attributed to Yu. V. Orlov.

8 recordsLinked to original sources

arXiv2020

The energies and ANCs for 5Li resonances deduced from experimental p-$α$ scattering phase shifts using the effective-range and $Δ$ methods

Recently a new $Δ$ method for deducing the energy and asymptotic normalization coefficient (ANC) from phase-shift data has been formulated and applied to resonance states. This differs from the conventional effective-range function (ERF) method by fitting only the nuclear part of the ERF. It also differs from the method which was proposed for bound states by Ramírez Suárez and Sparenberg (see Ref. below) which also named the $Δ$ method where a pole condition defines by the Eq. $Δ_l=0$ ($Δ_l$ is the function in the ERF determined only by the scattering phase shift). Here the standard pole condition, including the Coulomb part into the relate equation, is used for a resonant state. It has been shown that the ERF method does not work for large-charge colliding nuclei. Moreover, even for lower charges it is not clear that the results of the ERF method are accurately enough. The Coulomb part forms a background, which smooths an ERF energy dependence. Therefore, one needs to find when the ERF method becomes inaccurate and this requires recalculating some published results by the $Δ$ method. This project has already been started in a recent paper for resonances in the $α$-$α$ scattering. Here this method is applied using the $Δ_l$-function fittings to the experimental $p$-${}^4$He scattering phase-shift data in the $P_{3/2}$ and $P_{1/2}$ resonance states. The calculation results are compared with those obtained earlier by the ERF method. The main changes concern resonance energy and width.

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arXiv2019

An essential singularity of the cotangent of the Coulomb-nuclear phase shift, and a finite limit of the nuclear part of the effective-range function derived at zero energy

The Coulomb-nuclear phase shift $δ^{(cs)}_l$, $\cotδ^{(cs)}_l$ and a finite limit of the nuclear part $Δ_l(k)$ of the effective-range function (ERF) are derived for an arbitrary orbital momentum $l$ when energy $E\rightarrow0$. It is proved that $\cotδ^{(cs)}_l$ has an essential singularity at zero energy, but $Δ_l(k)$ does not. The explicit finite limit of $Δ_l(0)$ is found. The property of $Δ_l(k)$ as a meromorphic function makes possible the analytical continuation of a re-normalized scattering amplitude from the physical energy region to a bound state pole. Then the asymptotic normalization coefficients (ANC) can be deduced from experimental phase-shift data and applied to radiative capture processes which are important in nuclear astrophysics for new elements creation. Our results are in agreement with the results published for $S$ wave scattering.

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arXiv2018

Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function

Recently, a new $Δ$ method for the calculation of asymptotic normalization coefficients (ANC) from phase-shift data has been formulated, proved and used for bound states. This method differs from the conventional one by fitting only the nuclear part of the effective-range function which includes a partial phase shift. It should be applied to large-charge nuclei when the conventional effective-range expansion or the Padé-approximations using the effective-range function $K_l(k^2)$ fitting do not work. A typical example is the nucleus vertex $α+^{12}$C $\longleftrightarrow ^{16}$O. Here we apply the $Δ$ method, which totally excludes the effective-range function, to isolated resonance states. In fact, we return to the initial renormalized scattering amplitude with a denominator which defines the well-known pole condition. Concrete calculations are made for the resonances observed in the $^3$He-$^4$He, $α$-$α$, and $α$-$^{12}$C collisions. We use the experimental phase-shift and resonant energy data including their uncertainties and find the ANC variations for the states considered. The corresponding results are in a good agreement with those for the $S$-matrix pole method which uses the differing formalism. The simple formula for narrow resonances given in the literature is used to check the deduced results. The related ANC function clearly depends on the resonance energy ($E_0$) and width ($Γ$), which is used to find the ANC uncertainty ($Δ$ANC) through the energy ($ΔE_0$) and the width ($ΔΓ$) uncertainties.We also discuss the $Δ$ method differences between bound and resonance states pole conditions.

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arXiv2017

Algorithm for the asymptotic nuclear coefficients calculations using phase shift data for charged particles scattering

A new algorithm for the asymptotic nuclear coefficients calculation, which we call the $Δ$-method, is proved and developed. This method was proposed in Ref. [O. L. Ramírez Suárez and J.-M. Sparenberg, arXiv: 1602.04082 [nucl-th] (2016)] but no proof was given. We apply it to the bound state situated near the channel threshold when the Sommerfeld parameter is quite large within the experimental energy region. As a result, the value of the conventional effective-range function $K_l(k^2)$ is actually defined by the Coulomb term. One of the resulting effects is the wrong description of energy behavior of the elastic scattering phase shift $δ_l$ reproduced from the fitted total effective-range function $K_l(k^2)$. This leads to an improper value of the asymptotic normalization coefficient (ANC) value. No such problem arises if we fit only the nuclear term. The difference between the total effective-range function and the Coulomb part at real energies is the same as the nuclear term. Then we can proceed using just this $Δ$-method to calculate the pole position values and the ANC. We apply it to the vertices $^4\rm{He}+ {^{12}\rm{C}}\longleftrightarrow {^{16}\rm{O}}$ and $^3\rm{He}+ {^4\rm{He}}\longleftrightarrow {^7\rm{Be}}$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the $^{16}\rm{O}$ bound final states as well as to the $^7\rm{Be}\longleftrightarrow {^7\rm{Be}}$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the $^{16}\rm{O}$ bound final states as well as to the $^7\rm{Be}$.

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arXiv2016

Asymptotic normalization coefficients of resonant and bound states from the phase shifts for $αα$ and $α^{12}\rm C$ scattering

Recently we have published a paper [Irgaziev, Phys. Rev. C 91, 024002 (2015)] where the $S$-matrix pole method (SMP) which is only valid for resonances has been developed to derive a new explicit expression for the asymptotic normalization coefficient (ANC), and is applied to the low-energy resonant states of nucleon$+α$ and $α+^{12}\rm{C}$ systems. The SMP results are compared with the effective-range expansion method (EFE) results. In the present paper the SMP and EFE plus the Padé-approximation are applied to study the excited 2$^+$ resonant states of $^{8}\rm{Be}$. A contradiction is found between descriptions of the experimental phase shift data for $αα$ scattering and of the $^{8}\rm{Be}$ resonant energy for 2$^+$ state. Using the EFE method, we also calculate the ANC for the $^{8}\rm{Be}$ ground 0$^+$ state with a very small width. This ANC agrees well with the value calculated using the known analytical expression for narrow resonances. In addition, for the $α+^{12}\rm{C}$ states1$^-$ and 3$^-$ the SMP results are compared with the Padé-approximation results. We find that the Padé-approximation improves a resonance width description compared with the EFE results. The EFE method is also used to calculate the ANCs for the bound $^{16}\rm{O}$ ground 0$^+$ state and for the excited 1$^-$ and 2$^+$ levels which are situated near the threshold of $α+^{12}\rm{C}$ channel.

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arXiv2015

Resonance-state properties from a phase shift analysis with the $S$-matrix pole method and the effective-range method

Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing an important role in nuclear physics and astrophysics. We derive a new useful relationship between ANC of the Gamow radial wave function and the renormalized (due to the Coulomb interaction) Coulomb-nuclear partial scattering amplitude. We use an analytical approximation in the form of a series for the nonresonant part of the phase shift which can be analytically continued to the point of an isolated resonance pole in the complex plane of the momentum. Earlier, this method which we call the $S$-matrix pole method was used by us to find the resonance pole energy. We find the corresponding fitting parameters for the $^5\rm{He},\,^5\rm{Li}$, and $^{16}\rm{O}$ concrete resonance states. Additionally, based on the theory of the effective range, we calculate the parameters of the $p_{3/2}$ and $p_{1/2}$ resonance states of the nuclei $^5\rm{He}$ and $^5\rm{Li}$ and compare them with the results obtained by the $S$-matrix pole method. ANC values are found which can be used to calculate the reaction rate through the $^{16}\rm{O}$ resonances which lie slightly above the threshold for the $α^{12}\rm{C}$ channel.

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arXiv2011

Effect of Coulomb Forces on the Position of the Pole in the Scattering Amplitude and on Its Residue

Explicit expressions of the vertex constant for the decay of a nucleus into two charged particles for an arbitrary orbital momentum $l$ are derived for the standard expansion of the effective-range function $K_l(k^2)$, as well as when the function $K_0(k^2)$ has a pole. As physical examples, we consider the bound state of the nucleus ${}^3\rm{He}$ and the resonant states of the nuclei ${^2}$He and ${^3}$He in the s-wave, and those of ${}^5\rm{He}$ and ${}^5\rm{Li}$ in the p-wave. For the systems $Np$ and $Nd$ the pole trajectories are constructed in the complex planes of the momentum and of the renormalized vertex constant. They correspond to a transition from the resonance state to the virtual state while the Coulomb forces gradually decrease to zero.

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arXiv2009

Bound, virtual and resonance $S$-matrix poles from the Schrödinger equation

A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schrödinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to\infty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance $^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and $^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{\rm F}$

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