Long-range interatomic interactions: Oscillatory tails and hyperfine perturbations

We study the long-range interaction between two hydrogen atoms, in both the van der Waals and Casimir-Polder regimes. The retardation regime is reached when the finiteness of the speed of light becomes relevant. Provided that both atoms are in the ground states, the retardation regime is achieved when the interatomic distance, R, is larger than 137 a₀, where a₀ is the Bohr radius. To study the interaction between two hydrogen atoms in 1S and 2S states, we differentiate three different ranges for the interatomic distance: van der Waals range (a₀ « R « a₀/α, where α is the fine structure constant), the intermediate or Casimir-Polder range (a₀/α « R « ħc/L, where L is the Lamb shift energy), and the very long or Lamb shift range (R » ħc/L). We also study the Dirac-δ perturbation potential acting on the metastable excited states in the context of hyperfine splitting. The |2P1/2⟩ levels, which are displaced from the reference 2S-levels just by the Lamb shift, make the study of hyperfine resolved 2S-2S system very interesting. Each S and P state have a hyperfine singlet and a triplet. Thus, there are 8-hyperfine states per hydrogen atom and 8 x 8 = 64 states in the two atom system. The Hamiltonian matrix of the quasi-degenerate 2S-2S system is thus a (64 x 64)-matrix. Our treatment, which profits from adjacency graphs, allows us to do the hyperfine-resolved calculation. We examine the evolution of the energy levels in the hyperfine subspaces. We notice that there is a possibility of level crossings in higher dimensional quantum mechanical systems, which is a breakdown of the non-crossing theorem. For higher excited reference states, we match the scattering amplitude and effective Hamiltonian of the system. In the Lamb-shift range, we find an oscillatory term whose magnitude falls off as R⁻² and dominates the Wick-rotated term, which otherwise has a retarded Casimir-Polder type of interaction --Abstract, page iii

Long-Range Interactions of Hydrogen Atoms in Excited States. I. 2S-1S Interactions and Dirac-δ Perturbations

The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C6 (2S ;1 S ) describing the interaction of metastable atomic hydrogen ( 2 S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a0 ≪ R ≪ a0 / α , where a0 = ℏ / α m c is the Bohr radius and α is the fine-structure constant, one finds the symmetry-dependent result E2S;1S ( R ) ≈ ( - 176.75 ± 27.98 ) Eh( α0 / R )6 (Eh denotes the Hartree energy). In the Casimir-Polder range a0 / α ≪ R ≪ ℏ c / L , where L ≡ E (2S1/2 ) - E (2P1 / 2 ) is the Lamb shift energy, one finds E2S;1S ( R ) ≈ ( - 121.50 ± 46.61 ) Eh ( a0 / R )6 . In the the Lamb shift range R ≫ ℏ c / L , we find an oscillatory tail with a negligible interaction energy below 10-36 Hz . Dirac- δ perturbations to the interaction are also evaluated and results are given for all asymptotic distance ranges; these effects describe the hyperfine modification of the interaction or, expressed differently, the shift of the hydrogen 2 S hyperfine frequency due to interactions with neighboring 1 S atoms. The 2 S hyperfine frequency has recently been measured very accurately in atomic beam experiments

Long-Range Interactions of Hydrogen Atoms in Excited States. II. Hyperfine-Resolved 2S-2S Systems

The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasidegenerate 2P1/2 levels that are removed from the 2S states only by the Lamb shift. The total Hamiltonian of the system is composed of the van der Waals Hamiltonian, the Lamb shift, and the hyperfine effects. The van der Waals shift becomes commensurate with the 2S-2P3/2 fine-structure splitting only for close approach (R \u3c 100a0, where a0 is the Bohr radius) and one may thus restrict the discussion to the levels with n = 2 and J = 1/2 to a good approximation. Because each S or P state splits into an F = 1 triplet and an F = 0 hyperfine singlet (eight states for each atom), the Hamiltonian matrix a priori is of dimension 64. A careful analysis of the symmetries of the the problem allows one to reduce the dimensionality of the most involved irreducible submatrix to 12. We determine the Hamiltonian matrices and thleading-order van der Waals shifts for states that are degenerate under the action of the unperturbed Hamiltonian (Lamb shift plus hyperfine structure). The leading first- and second-order van der Waals shifts lead to interaction energies proportional to 1/R3 and 1/R6 and are evaluated within the hyperfine manifolds. When both atoms are metastable 2S states, we find an interaction energy of order EhΧ(a0/R)6, where Eh and L are the Hartree and Lamb shift energies, respectively, and Χ = Eh/L ≈ 6.22 x 106 is their ratio

Long-Range Interactions of Hydrogen Atoms in Excited States. I. 2S-1S Interactions and Dirac-δ Perturbations

The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C6 (2S ;1 S ) describing the interaction of metastable atomic hydrogen ( 2 S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a0 ≪ R ≪ a0 / α , where a0 = ℏ / α m c is the Bohr radius and α is the fine-structure constant, one finds the symmetry-dependent result E2S;1S ( R ) ≈ ( - 176.75 ± 27.98 ) Eh( α0 / R )6 (Eh denotes the Hartree energy). In the Casimir-Polder range a0 / α ≪ R ≪ ℏ c / L , where L ≡ E (2S1/2 ) - E (2P1 / 2 ) is the Lamb shift energy, one finds E2S;1S ( R ) ≈ ( - 121.50 ± 46.61 ) Eh ( a0 / R )6 . In the the Lamb shift range R ≫ ℏ c / L , we find an oscillatory tail with a negligible interaction energy below 10-36 Hz . Dirac- δ perturbations to the interaction are also evaluated and results are given for all asymptotic distance ranges; these effects describe the hyperfine modification of the interaction or, expressed differently, the shift of the hydrogen 2 S hyperfine frequency due to interactions with neighboring 1 S atoms. The 2 S hyperfine frequency has recently been measured very accurately in atomic beam experiments

Long-Range Interactions of Hydrogen Atoms in Excited States. I. 2S-1S Interactions and Dirac-δ Perturbations

The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C6 (2S ;1 S ) describing the interaction of metastable atomic hydrogen ( 2 S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a0 ≪ R ≪ a0 / α , where a0 = ℏ / α m c is the Bohr radius and α is the fine-structure constant, one finds the symmetry-dependent result E2S;1S ( R ) ≈ ( - 176.75 ± 27.98 ) Eh( α0 / R )6 (Eh denotes the Hartree energy). In the Casimir-Polder range a0 / α ≪ R ≪ ℏ c / L , where L ≡ E (2S1/2 ) - E (2P1 / 2 ) is the Lamb shift energy, one finds E2S;1S ( R ) ≈ ( - 121.50 ± 46.61 ) Eh ( a0 / R )6 . In the the Lamb shift range R ≫ ℏ c / L , we find an oscillatory tail with a negligible interaction energy below 10-36 Hz . Dirac- δ perturbations to the interaction are also evaluated and results are given for all asymptotic distance ranges; these effects describe the hyperfine modification of the interaction or, expressed differently, the shift of the hydrogen 2 S hyperfine frequency due to interactions with neighboring 1 S atoms. The 2 S hyperfine frequency has recently been measured very accurately in atomic beam experiments

Occluded Coronary Artery among Non-ST Elevation Myocardial Infarction Patients in Department of Cardiology of a Tertiary Care Centre: A Descriptive Cross-sectional Study

Introduction: Non-ST elevation myocardial infarction is frequently thought to be caused by incomplete blockage of the culprit artery, whereas ST elevation myocardial infarction is frequently thought to be caused by total occlusion of the culprit artery. The objective of the study was to find out the prevalence of occluded coronary arteries among non-ST elevation myocardial infarction patients department of cardiology of a tertiary care centre. Methods: A descriptive cross-sectional study was conducted among non-ST elevation myocardial infarction patients in a tertiary care centre from 22 June 2020 to 21 June 2021 after taking ethical approval from the Institutional Review Committee [Reference number: 4271 (6-11) E2 076/077]. A total of 196 patients were included in the study by simple randomized sampling. Data on the patient’s clinical profile, angiographic findings, and in-hospital complications were recorded. Point estimate and 95% Confidence Interval were calculated. Results: Among 126 non-ST elevation myocardial infarction patients included in the study, the prevalence of occluded coronary artery was 41 (32.54%) (24.36-40.72, 95% Confidence Interval). Conclusions: The prevalence of occluded coronary arteries was similar to the studies done in similar settings

Optoplasmonics of Single-Walled Carbon Nanotube Thin Films

An ultrathin film capable of exhibiting material properties across and around two different dimensions by bridging two-dimensionality frameworks, called a trans-dimensional (TD) material, can be an exceptional tool to tune various electronic and optoplasmonic properties of a system that are unattainable from either dimension. Taking an example of the planar periodic arrangement of single-walled carbon nanotube (SWCNT) TD films, we semi-analytically calculated their dynamical conductivities and dielectric responses as a function of the incident photon frequency and the SWCNT’s radius using the many-particles Green’s function formalism within the Matsubara frequency technique. The periodic array of SWCNTs has an anisotropic dielectric response, which is almost a constant and the same as that of the host dielectric medium in the perpendicular direction of the alignment of the SWCNT array due to the depolarization effect that SWCNTs have. However, the dielectric response functions depend on the incident photon energy in addition to the film’s thickness, the SWCNT’s sparseness, inhomogeneity, and the SWCNT’s diameter. The energy difference between the resonant absorption peak and the plasmonic peak varies with the thickness of the film. Varying the length of the CNTs, we also observed that the exciton–plasmon coupling strength increases with the increase in length of the SWCNTs. The metallic SWCNT-containing films have comparatively pronounced plasmon resonance peaks at low photon energy than semiconducting SWCNT-containing films. Both metallic and semiconducting SWCNT-consisting films have negative refraction for a wide range of energy, making them good candidates for metamaterials. © 2025 Elsevier B.V., All rights reserved

Optoplasmonics of Single-Walled Carbon Nanotube Thin Films

An ultrathin film capable of exhibiting material properties across and around two different dimensions by bridging two-dimensionality frameworks, called a trans-dimensional (TD) material, can be an exceptional tool to tune various electronic and optoplasmonic properties of a system that are unattainable from either dimension. Taking an example of the planar periodic arrangement of single-walled carbon nanotube (SWCNT) TD films, we semi-analytically calculated their dynamical conductivities and dielectric responses as a function of the incident photon frequency and the SWCNT’s radius using the many-particles Green’s function formalism within the Matsubara frequency technique. The periodic array of SWCNTs has an anisotropic dielectric response, which is almost a constant and the same as that of the host dielectric medium in the perpendicular direction of the alignment of the SWCNT array due to the depolarization effect that SWCNTs have. However, the dielectric response functions depend on the incident photon energy in addition to the film’s thickness, the SWCNT’s sparseness, inhomogeneity, and the SWCNT’s diameter. The energy difference between the resonant absorption peak and the plasmonic peak varies with the thickness of the film. Varying the length of the CNTs, we also observed that the exciton–plasmon coupling strength increases with the increase in length of the SWCNTs. The metallic SWCNT-containing films have comparatively pronounced plasmon resonance peaks at low photon energy than semiconducting SWCNT-containing films. Both metallic and semiconducting SWCNT-consisting films have negative refraction for a wide range of energy, making them good candidates for metamaterials

Knowledge of Unsafe Abortion among Female Students in Nepal

The term 'abortion' is a deliberate termination of unwanted human pregnancy. To save maternal health and life and control population growth, abortion has been legally permitted in Nepal since 2002. Most of the female youths stay away from home and are vulnerable to risky behavior regarding sex related matters. They have no proper knowledge about unsafe abortion. The objective of this article is to investigate the knowledge about unsafe abortion among the female youths in Pokhara. A descriptive cross-sectional study was conducted among 133 BBS first-year female students by using the simple random sampling. A self-administered questionnaire was prepared to assess the participants’ socio-demographic factors along with their knowledge about unsafe abortion. The association of knowledge was categorized with selected variables. Out of the 133 respondents, 49.6 percent were from the age group 19-20, 46.6 percent from the group of Janjati, 78.2 percent from the group of Hindu followers and 86.5 percent from the single respondents. The majority of the respondents (71.4 percent) were found to have the knowledge that over-bleeding was the consequence of abortion. Among the total respondents, 58 percent respondents had good knowledge about unsafe abortion and 15 percent had poor knowledge about unsafe abortion. No significant connection of age with knowledge of unsafe abortion has been observed during the study as the p value is greater than 0.05 at 95 confidence level, but other variables like caste, religion, place of residence and marital status have been found to have a significant relation with knowledge of unsafe abortion because p value is smaller than 0.05 at 95 confidence level.</jats:p

Clinical profile, management and outcome of pulmonary embolism in Shahid Gangalal National Heart Centre, Kathmandu, Nepal

Background and aims: Pulmonary embolism (PE) is associated with a significant mortality and morbidity. We aim to study clinical profile, management and outcome of PE at Shahid Gangalal National heart Centre, Kathmandu, Nepal. Methods: It was a retrprospective, single centre study, conducted from January 2015 to December 2016. Haemodynamics was used for risk Simplified, PESI score, predisposing factors, symptoms, clinical features at the time of admission, ECG features, echocardiogram, treatment received and the outcome were reviewed. Results: During the study period 23 cases of PE were admitted. Nine were males and 14 were females. Eleven patients were diagnosed as provoked PE. High risk PE was diagnosed in four patients, Non-high risk in 19 patients. The most common clinical presentation was shortness of breath. The most common finding in ECG is sinus tachycardia followed by ST-T changes in V1-V3. Eight patient had SPO2 less than 90%. Most of the patients had a normal chest radiograph. Echocardiography revealed dilated RA and RV in 20 patients.All high risk PE patients were thrombolyzed with streptokinase. All patients who were diagnosed as Non-high risk PE were treated with LMWH. All the patients were treated with oral anticoagulants. Mean hospital stay was 9.7 ± 4.9 days. Two patients died during hospital stay. S-PESI score was 1.4 ± 0.9 respectively. Mean warfarin dose at the time of discharge was 5.9 ± 1.6 mg. Conclusion: PE is an under diagnosed clinical problem world over. Suspicion is the most important part to come to the diagnosis of PE. Keywords: Acute pulmonary embolism, High risk PE, Provoked PE, Simplified PESI scor