scholarly journals Third-order non-Coulomb correction to the S-wave quarkonium wave functions at the origin

2008 ◽  
Vol 658 (5) ◽  
pp. 222-229 ◽  
Author(s):  
M. Beneke ◽  
Y. Kiyo ◽  
K. Schuller
Keyword(s):  
Wave Functions ◽  
Coulomb Correction ◽  
S Wave ◽  
Third Order

A perturbation calculation of properties of the 2 pπ state of HeH 2+

1957 ◽  
Vol 240 (1221) ◽  
pp. 274-283 ◽  
Keyword(s):  
Dipole Moment ◽  
Total Energy ◽  
Second Order ◽  
Wave Functions ◽  
Quadrupole Moments ◽  
Perturbation Calculation ◽  
Third Order ◽  
The Third ◽  
Fifth Order ◽  
Kinetic And Potential Energies

A perturbation calculation, valid in the limit of large separations, of various properties of the 2 pπ state of HeH 2+ is carried out. The total energy and the kinetic and potential energies are calculated to the fifth order, the dipole moment to the third order and the quadrupole moments to the second order and the results compared with those obtained using exact and variationally determined two-centre wave functions. Some results are also given for the 2 pπ u and 3 dπ g states of H + 2 and the influence of nuclear symmetry at large separations is briefly discussed.

Comparative study of the energy dependent and independent two-nucleon interactions — A supersymmetric approach

2014 ◽  
Vol 23 (08) ◽  
pp. 1450039 ◽  
Author(s):  
U. Laha ◽  
J. Bhoi
Keyword(s):  
Factorization Method ◽  
Nucleon Nucleon ◽  
Wave Functions ◽  
S Wave ◽  
Starting Point ◽  
Phase Function Method ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Energy Dependent ◽  
Supersymmetric Approach

By exploiting supersymmetry inspired factorization method nucleon–nucleon (n–n) potentials, both energy dependent and independent, in the partial waves 1P1 and 3P1 are generated by judicious use of appropriate ground state wave functions and interactions. The energy independent Hulthen and energy dependent equivalent local Yamaguchi potentials and their corresponding S-wave functions are used as the starting point of our calculation. The scattering phase shifts are computed for the constructed potentials through Phase Function Method (PFM) and compared with the standard results to examine the merit of our approach to the problem.

scholarly journals Mass spectrum and strong decays of tetraquark $${\bar{c}}{\bar{s}} qq$$ states

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Guang-Juan Wang ◽  
Lu Meng ◽  
Li-Ye Xiao ◽  
Makoto Oka ◽  
Shi-Lin Zhu
Keyword(s):  
Mass Spectrum ◽  
Hyperfine Interactions ◽  
Large Mass ◽  
Mass Splitting ◽  
Wave Functions ◽  
Tetraquark State ◽  
Strong Decay ◽  
S Wave ◽  
Different Color ◽  
Partner State

AbstractWe systematically study the mass spectrum and strong decays of the S-wave $${\bar{c}}{\bar{s}} q q$$ c ¯ s ¯ q q states in the compact tetraquark scenario with the quark model. The key ingredients of the model are the Coulomb, the linear confinement, and the hyperfine interactions. The hyperfine potential leads to the mixing between different color configurations, and to the large mass splitting between the two ground states with $$I(J^P)=0(0^+)$$ I ( J P ) = 0 ( 0 + ) and $$I(J^P)=1(0^+)$$ I ( J P ) = 1 ( 0 + ) . We calculate their strong decay amplitudes into the $${\bar{D}}^{(*)}K^{(*)}$$ D ¯ ( ∗ ) K ( ∗ ) channels with the wave functions from the mass spectrum calculation and the quark-interchange method. We examine the interpretation of the recently observed $$X_0(2900)$$ X 0 ( 2900 ) as a tetraquark state. The mass and decay width of the $$I(J^P)=1(0^+)$$ I ( J P ) = 1 ( 0 + ) state are $$M=2941$$ M = 2941 MeV and $$\Gamma _X=26.6$$ Γ X = 26.6 MeV, respectively, which indicates that it might be a good candidate for $$X_0(2900)$$ X 0 ( 2900 ) . Meanwhile, we also obtain an isospin partner state $$I(J^P)=0(0^+)$$ I ( J P ) = 0 ( 0 + ) with $$M=2649$$ M = 2649 MeV and $$\Gamma _{X\rightarrow {\bar{D}} K}=48.1$$ Γ X → D ¯ K = 48.1 MeV, respectively. Future experimental search for X(2649) will be very helpful.

Positronium formation in low-energy positron–helium scattering

1996 ◽  
Vol 74 (7-8) ◽  
pp. 335-342 ◽  
Author(s):  
J. W. Humberston ◽  
P. Van Reeth
Keyword(s):  
Elastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Wave Functions ◽  
Positronium Formation ◽  
Recent Analysis ◽  
S Wave ◽  
Small Magnitude ◽  
Formation Cross Section ◽  
Positron Collisions

Detailed investigations were made of positron collisions with helium atoms in the Ore gap using a two-channel version of the Kohn variational method with very flexible trial wave functions and accurate correlated helium-target wave functions. Accurate values of the s-wave elastic scattering and positronium-formation cross sections are presented, together with preliminary values of the cross sections for s-wave scattering. The s-wave positronium-formation cross section in helium displays a remarkable similarity in both magnitude and energy dependence to the corresponding cross section in positron–hydrogen scattering, with a rapid rise from the positronium-formation threshold and a more gradual rise thereafter. Its small magnitude is consistent with the findings of a recent analysis of experimental measurements of the positronium-formation cross section. Calculations of the s-wave elastic-scattering cross section above and below the positronium-formation threshold reveal a Wigner "rounded step" at the threshold itself.

scholarly journals Many-body calculation of helium 1D–3D term intervals for 1snd (n = 12 ∼ 20) high Rydberg states

2006 ◽  
Vol 84 (12) ◽  
pp. 1097-1106
Author(s):  
Liming He ◽  
Wei Cao
Keyword(s):  
Bound States ◽  
Perturbation Expansion ◽  
Hartree Equation ◽  
Wave Functions ◽  
Many Body ◽  
Zeroth Order ◽  
Third Order ◽  
Many Body Perturbation Theory ◽  
Integral Processing ◽  
Schrödinger Perturbation

With many-body perturbation theory, 1D–3D term intervals of helium 1snd (n = 12 ∼ 20) configurations are calculated. Based on two different models, Rayleigh-Schrodinger perturbation expansion terms consisting of bound states only, and those of continua are evaluated, respectively. As for bound states, zeroth-order wave functions are strictly generated from self-iteration solutions of the Hartree equation and residues of infinite expansion series are dealt with by the integral processing method, while a simplified hydrogen potential is adopted to get the continua. Using Rayleigh–Schrodinger expansions, we evaluate exchange energy up to third-order terms. It is found that level splittings are mainly attributed to summations over bound states. The fine-structure level splittings yielded here are found to agree quite well with experimental results.PACS Nos.: 31.15.Md, 32.10Fn, 02.60Ed

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