Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z
The question of stability of a given quantum system made up of charged particles is of fundamental interest in atomic, molecular, and nuclear physics. In this work, the stability for the negatively charged positronium (Ps)-like ions or the three-body system (<inline-formula> <math display=&...
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2019-06-01
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doaj-e1cfe9b71d584312831e124bae4cbe412020-11-24T23:53:28ZengMDPI AGAtoms2218-20042019-06-01725310.3390/atoms7020053atoms7020053Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying ZSabyasachi Kar0Yu-Shu Wang1Yang Wang2Yew Kam Ho3Department of Physics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Physics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Physics, Harbin Institute of Technology, Harbin 150001, ChinaInstitute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, TaiwanThe question of stability of a given quantum system made up of charged particles is of fundamental interest in atomic, molecular, and nuclear physics. In this work, the stability for the negatively charged positronium (Ps)-like ions or the three-body system (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <msup> <mi>e</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> </mrow> </semantics> </math> </inline-formula>) with Yukawa potentials is studied using correlated exponential wavefunctions based on the Ritz variational method. We obtained the critical screening parameter <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>μ</mi> <mi>C</mi> </msub> </mrow> </semantics> </math> </inline-formula> as a function of the continuously varied nuclear charge <inline-formula> <math display="inline"> <semantics> <mi>Z</mi> </semantics> </math> </inline-formula>, the critical nuclear charge <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>Z</mi> <mi>C</mi> </msub> </mrow> </semantics> </math> </inline-formula> as a function of the screening parameter <inline-formula> <math display="inline"> <semantics> <mi>μ</mi> </semantics> </math> </inline-formula>, and the ionization energies in terms of the screening parameter <inline-formula> <math display="inline"> <semantics> <mi>μ</mi> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mi>Z</mi> </semantics> </math> </inline-formula>. The critical nuclear charge for the bare Coulomb system (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <msup> <mi>e</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> </mrow> </semantics> </math> </inline-formula>) obtained using 700-term correlated exponential wavefunctions is in accord with the reported results. The ionization energy, <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>μ</mi> <mi>C</mi> </msub> </mrow> </semantics> </math> </inline-formula>, and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>Z</mi> <mi>C</mi> </msub> </mrow> </semantics> </math> </inline-formula> for the Yukawa system (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <msup> <mi>e</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> </mrow> </semantics> </math> </inline-formula>) exhibit interesting behaviors. The present study describes the possible nonexistence of Borromean binding as well as Efimov states. The possible existence of quasi-bound resonances states for the negatively charged screened Ps-like ions is briefly discussed.https://www.mdpi.com/2218-2004/7/2/53critical stabilitycritical nuclear chargecritical screening parameterYukawa potentialsDebye potentialspositronium negative ionexponentially correlated wavefunctionsvariational method |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sabyasachi Kar Yu-Shu Wang Yang Wang Yew Kam Ho |
| spellingShingle |
Sabyasachi Kar Yu-Shu Wang Yang Wang Yew Kam Ho Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z Atoms critical stability critical nuclear charge critical screening parameter Yukawa potentials Debye potentials positronium negative ion exponentially correlated wavefunctions variational method |
| author_facet |
Sabyasachi Kar Yu-Shu Wang Yang Wang Yew Kam Ho |
| author_sort |
Sabyasachi Kar |
| title |
Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z |
| title_short |
Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z |
| title_full |
Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z |
| title_fullStr |
Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z |
| title_full_unstemmed |
Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z |
| title_sort |
critical stability of the negatively charged positronium-like ions with yukawa potentials and varying z |
| publisher |
MDPI AG |
| series |
Atoms |
| issn |
2218-2004 |
| publishDate |
2019-06-01 |
| description |
The question of stability of a given quantum system made up of charged particles is of fundamental interest in atomic, molecular, and nuclear physics. In this work, the stability for the negatively charged positronium (Ps)-like ions or the three-body system (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <msup> <mi>e</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> </mrow> </semantics> </math> </inline-formula>) with Yukawa potentials is studied using correlated exponential wavefunctions based on the Ritz variational method. We obtained the critical screening parameter <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>μ</mi> <mi>C</mi> </msub> </mrow> </semantics> </math> </inline-formula> as a function of the continuously varied nuclear charge <inline-formula> <math display="inline"> <semantics> <mi>Z</mi> </semantics> </math> </inline-formula>, the critical nuclear charge <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>Z</mi> <mi>C</mi> </msub> </mrow> </semantics> </math> </inline-formula> as a function of the screening parameter <inline-formula> <math display="inline"> <semantics> <mi>μ</mi> </semantics> </math> </inline-formula>, and the ionization energies in terms of the screening parameter <inline-formula> <math display="inline"> <semantics> <mi>μ</mi> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mi>Z</mi> </semantics> </math> </inline-formula>. The critical nuclear charge for the bare Coulomb system (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <msup> <mi>e</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> </mrow> </semantics> </math> </inline-formula>) obtained using 700-term correlated exponential wavefunctions is in accord with the reported results. The ionization energy, <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>μ</mi> <mi>C</mi> </msub> </mrow> </semantics> </math> </inline-formula>, and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>Z</mi> <mi>C</mi> </msub> </mrow> </semantics> </math> </inline-formula> for the Yukawa system (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <msup> <mi>e</mi> <mo>+</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> <mo>,</mo> <msup> <mi>e</mi> <mo>−</mo> </msup> </mrow> </semantics> </math> </inline-formula>) exhibit interesting behaviors. The present study describes the possible nonexistence of Borromean binding as well as Efimov states. The possible existence of quasi-bound resonances states for the negatively charged screened Ps-like ions is briefly discussed. |
| topic |
critical stability critical nuclear charge critical screening parameter Yukawa potentials Debye potentials positronium negative ion exponentially correlated wavefunctions variational method |
| url |
https://www.mdpi.com/2218-2004/7/2/53 |
| work_keys_str_mv |
AT sabyasachikar criticalstabilityofthenegativelychargedpositroniumlikeionswithyukawapotentialsandvaryingz AT yushuwang criticalstabilityofthenegativelychargedpositroniumlikeionswithyukawapotentialsandvaryingz AT yangwang criticalstabilityofthenegativelychargedpositroniumlikeionswithyukawapotentialsandvaryingz AT yewkamho criticalstabilityofthenegativelychargedpositroniumlikeionswithyukawapotentialsandvaryingz |
| _version_ |
1725469545843392512 |