Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:nucl-th/9803046

Higher Order Hadronic Energy Level Shifts in Protonium

Xinwei Kong, F. Ravndal

Published Mar 23, 1998• 0 citations
arXivHTMLPDF

Abstract

Using effective field theory for a proton and antiproton bound in a Coulomb potential, the shift of the ground state energy level is calculated to arbitrary order in the scattering length. Including the next order contact interaction, the correction due to the effective range parameter can also be obtained.
DOI
10.48550/arxiv.nucl-th/9803046

Related papers

Low-energy antiproton scattering by atoms and Coulomb level shifts

Olgierd Dumbrajs

A relationship between the low-energy antiproton-atom scattering parameters and Coulomb level shifts is derived. The corresponding scattering lengths are calculated for the p\ifmmode\bar\else\textasciimacron\fi{}-${\mathrm{He}}^{+}$ system on the basis of energy level shifts evaluated earlier by means of the Born-Oppenheimer approximation.

Physical Review A•Jul 1, 1985•1 citation

Proton-proton scattering on a quantum computer

Ratna Khadka, Gautam Rupak

Scattering of charged particles is ubiquitous in nuclear physics. We calculate the proton-proton $s$-wave phase shift at low energy relevant to solar physics. The phase shift is calculated from the ratio of the regular and irregular solutions to the radial Schrödinger equation on a hard spherical wall boundary for the ground state. The ground state energy is calculated using a hybrid quantum-classical variational algorithm. A theory with short-ranged nuclear interaction in the presence of the long-ranged Coulomb force is used to describe the scattering. The theory is discretized on a spatial lattice for adaptation to the quantum computer in the second quantized language. The phase shifts at low momenta are accurately reproduced.

arXiv:2508.07986•Aug 11, 2025•0 citations

A typical oscillating perturbation on protonium

Herry Fridolin Lalus, Nila Prasetya Aryani

Abstract Protonium is a type of onium consisting of a proton (p) and an anti-proton ( <?CDATA $ \bar p $?> p ¯ ) which is called antiprotonic hydrogen. Since the proton and the anti-particle have the same mass, and each of them is a fermion, the Hamiltonian form of this system consists of the kinetic energy terms of each particle, the potential energy, and the spin interactions of both (hyperfine structure). To simplify the analysis, the Hamiltonian is then converted into a Hamiltonian which contains the relative motion terms of the two particles. This new Hamiltonian contains their reduced mass because the two particles orbit each other towards a certain center of mass. In the initial state, t < 0, the system is in the ground state and then at 0 < t < τ, the system is given a disturbance of the form <?CDATA $ V(t) = ({V_0} + {V_1}\,r\,\sin \theta \,{e^{i\phi }})\,\cos (\omega t)\,{\hat \sigma _p}.\hat x $?> V ( t ) = ( V 0 + V 1 r sin θ e i ϕ ) cos ( ω t ) σ ^ p . x ^ , where V 0 is a constant, V 1 is a constant and very small, <?CDATA $ {\hat \sigma _p} $?> σ ^ p is the Pauli matrix for proton, and <?CDATA $ \hat x $?> x ^ is the three-dimensional position operator in spherical coordinates. We analyze this system using a time-dependent perturbation theory that begins by defining the initial state, then calculating the transition amplitude for the new state when the perturbation is applied to the system. From the results of this calculation, we compute the system transition probability. We find that the transition probability of this system can only occur for the following quantum number terms, namely n even positive integer, l = 2,S = 1, and with the certain combinations of m and M.

Journal of Physics Conference Series•Jun 1, 2021•2 citations

Scattering Lengths Derived from Atomic Level Shifts in Light Antiprotonic Atoms

Olgierd Dumbrajs

Scattering lengths in the systems 4 He, 6 Li, 7 Li, 12 C, 16 O, 17 O, and 18 O are derived from the measurements of the strong interaction atomic level shifts in the corresponding antiprotonic atoms. The Coulomb corrections to the scattering lengths are evaluated and it is found that they are large.

Physica Scripta•Jun 1, 1985•30 citations

Low-energy antiproton interaction with helium

William R Gibbs

An ab initio potential for the interaction of the neutral helium atom with antiprotons and protons is calculated using the Born-Oppenheimer approximation. Using this potential, the annihilation cross section for antiprotons in the energy range 0.01 $\ensuremath{\mu}$eV to 1 eV is calculated.

arXiv:nucl-th/9705007•Physical Review A•Nov 1, 1997•8 citations

Possibility of a /sup 4/He/sub 2/ bound state, effective range theory, and very low energy He--He scattering

Yea-Hwang Uang, W. C. Stwalley

The best available intermolecular potential for helium by Aziz, Nain, Carley, Taylor, and McConville is shown here for the first time to have a /sup 4/He/sub 2/ bound state. Two numerical analyses, namely, eigenvalue solution and effective range theory, are used to support this conclusion. Unlike usual chemically bound species, the binding energy of this very weakly bound level is found to be only 8.3 x 10/sup -4/ K, which is four orders of magnitude smaller than the potential well depth epsilon = 10.8 K. The scattering length for He+He collisions, determined from effective range theory, is used to calculate the elastic cross section in the very low energy limit. The results (1.878 x 10/sup 5/ A/sup 2/ for /sup 4/He+/sup 4/He and 6.035 x 10/sup 2/ A for /sup 3/He+/sup 3/He) are consistent with measurements at the lowest velocities yet attained. In terms of the estimated uncertainties of the parameters of the potential of Aziz and co-workers, it is shown that it is very likely that a bound state of the /sup 4/He/sub 2/ molecule does in fact exist.

•May 15, 1982•0 citations
A relationship between the low-energy antiproton-atom scattering parameters and Coulomb level shifts is derived. The corresponding scattering lengths are calculated for the p\ifmmode\bar\else\textasciimacron\fi{}-He+{\mathrm{He}}^{+}He+ system on the basis of energy level shifts evaluated earlier by means of the Born-Oppenheimer approximation.
Scattering of charged particles is ubiquitous in nuclear physics. We calculate the proton-proton sss-wave phase shift at low energy relevant to solar physics. The phase shift is calculated from the ratio of the regular and irregular solutions to the radial Schrödinger equation on a hard spherical wall boundary for the ground state. The ground state energy is calculated using a hybrid quantum-classical variational algorithm. A theory with short-ranged nuclear interaction in the presence of the long-ranged Coulomb force is used to describe the scattering. The theory is discretized on a spatial lattice for adaptation to the quantum computer in the second quantized language. The phase shifts at low momenta are accurately reproduced.
Abstract Protonium is a type of onium consisting of a proton (p) and an anti-proton ( <?CDATA $ \bar p $?> p ¯ ) which is called antiprotonic hydrogen. Since the proton and the anti-particle have the same mass, and each of them is a fermion, the Hamiltonian form of this system consists of the kinetic energy terms of each particle, the potential energy, and the spin interactions of both (hyperfine structure). To simplify the analysis, the Hamiltonian is then converted into a Hamiltonian which contains the relative motion terms of the two particles. This new Hamiltonian contains their reduced mass because the two particles orbit each other towards a certain center of mass. In the initial state, t < 0, the system is in the ground state and then at 0 < t < τ, the system is given a disturbance of the form <?CDATA $ V(t) = ({V_0} + {V_1}\,r\,\sin \theta \,{e^{i\phi }})\,\cos (\omega t)\,{\hat \sigma _p}.\hat x $?> V ( t ) = ( V 0 + V 1 r sin θ e i ϕ ) cos ( ω t ) σ ^ p . x ^ , where V 0 is a constant, V 1 is a constant and very small, <?CDATA $ {\hat \sigma _p} $?> σ ^ p is the Pauli matrix for proton, and <?CDATA $ \hat x $?> x ^ is the three-dimensional position operator in spherical coordinates. We analyze this system using a time-dependent perturbation theory that begins by defining the initial state, then calculating the transition amplitude for the new state when the perturbation is applied to the system. From the results of this calculation, we compute the system transition probability. We find that the transition probability of this system can only occur for the following quantum number terms, namely n even positive integer, l = 2,S = 1, and with the certain combinations of m and M.
The best available intermolecular potential for helium by Aziz, Nain, Carley, Taylor, and McConville is shown here for the first time to have a /sup 4/He/sub 2/ bound state. Two numerical analyses, namely, eigenvalue solution and effective range theory, are used to support this conclusion. Unlike usual chemically bound species, the binding energy of this very weakly bound level is found to be only 8.3 x 10/sup -4/ K, which is four orders of magnitude smaller than the potential well depth epsilon = 10.8 K. The scattering length for He+He collisions, determined from effective range theory, is used to calculate the elastic cross section in the very low energy limit. The results (1.878 x 10/sup 5/ A/sup 2/ for /sup 4/He+/sup 4/He and 6.035 x 10/sup 2/ A for /sup 3/He+/sup 3/He) are consistent with measurements at the lowest velocities yet attained. In terms of the estimated uncertainties of the parameters of the potential of Aziz and co-workers, it is shown that it is very likely that a bound state of the /sup 4/He/sub 2/ molecule does in fact exist.