Cold hydrogen-hydrogen scattering using CCA model

Chakraborty, Sagnik; Sen, Anamika; Ghosh, Arnab

doi:10.1140/epjd/e2007-00239-9

Cited by 8 publications

(10 citation statements)

References 37 publications

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“…Therefore, the weak long-range magnetic dipolar interaction becomes important, providing a shift which depends on the geometry of the system. We present the first direct measurement of the difference between the singlet and triplet s-wave scattering lengths, which is in fair agreement with existing calculations [9,10]. Our experiments demonstrate that for H atoms with certain nuclear spin projections in a strong field the s-wave interaction vanishes, like in the case of fermions [6], and nuclear spin may be used to switch electron interactions on and off.…”

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confidence: 87%

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Clock Shift in High Field Magnetic Resonance of Atomic Hydrogen

et al. 2008

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We have measured electron spin resonance line shifts due to collisions in atomic hydrogen gas compressed to densities approximately 10(18) cm(-3) in a strong magnetic field (4.6 T). The shift in a doubly polarized gas is negligible, in contrast with a mixture of two hyperfine states. This difference is explained by properly including effects of quantum statistics in atomic collisions and magnetic dipolar effects. We report on the first direct measurement of the difference between the triplet and singlet s-wave scattering lengths a(t) - a(s) = 60(10) pm, which is in agreement with existing theories.

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supporting

confidence: 87%

“…This is in the range Áa ¼ 40-80 pm of calculated values [10] and better matches the theories where the reduced atomic mass is used to calculate interatomic potentials (i.e., Ref. [9] gives Áa ¼ 48 pm).…”

supporting

confidence: 77%

Clock Shift in High Field Magnetic Resonance of Atomic Hydrogen

et al. 2008

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“…From Eqs.(3) and (4) we find C ba = C ab = γem (a t − a s ) and ∆a = 30(5) pm. This is somewhat lower than the theoretical values ∆a = 42 − 55 pm for the difference in the scattering lengths [4][5][6].…”

contrasting

confidence: 64%

“…(3) and ( 4) we find C ba = C ab = γem (a t − a s ) and ∆a 30(5) pm. This is somewhat lower than the theoretical values ∆a = 42 − 55 pm for the difference in the scattering lengths [4][5][6]. This work was supported by the Russian Foundation for Basic Research, project no.…”

contrasting

confidence: 56%

Comment on “Clock Shift in High Field Magnetic Resonance of Atomic Hydrogen”

2010

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Ahokas et al.[1] measured the hyperfine frequency shifts in three-dimensional spin-polarized atomic hydrogen by means of ESR. In this Comment, we address their analysis of the interaction energy of the ground-state H atoms in different hyperfine states and show that the quoted difference Áa ¼ a t À a s between the triplet and singlet scattering lengths derived from the correctly measured shifts is overestimated by a factor of 2.Ahokas et al. observed the transitions a ! d and b ! c in the presence of the third-state atoms (b and a, respectively) and found the shifts of the corresponding resonance fields to be ÁB ad ¼ C ab n b þ C aa n a and ÁB bc ¼ C bb n b þ C ba n a with C ab % C ba ¼ 8ð2Þ Â 10 À19 cm 3 and C aa ; C bb ( C ba . To explain this observation, Ahokas et al. expressed the spin states of a pair of atoms in the jS; m S ; I; m I i basis, that is, in terms of electron and nuclear singlets and triplets. In particular, in the high-field limit, jabi ¼ 1 ffiffi 2 p ðje t ; n t i þ je t ; n s iÞ, jaci ¼ jbdi ¼ 1 2 ðje t ;n t i þ je t ;n s i þ je s ;n t i þ je s ;n s iÞ. At low temperature, only the symmetric components je t ; n t i and je s ; n s i contribute to (s-wave) scattering via the triplet V t and singlet V s interatomic potential, respectively.More specifically, the interaction energy of H atoms in different hyperfine states and (; ¼ a; b; c; d) is given by the second-quantization Hamiltonian (i; j ¼The wave function of two bosons must be symmetric,where the spatial and spin parts are, respectively, R AE ¼ 1 ffiffi 2 p ½c k ðr 1 Þc q ðr 2 Þ AE c q ðr 1 Þc k ðr 2 Þ and jiji AE ¼ 1 ffiffi 2 p ðjiji AE jjiiÞ. The use of the symmetric form (2) of the diatomic wave function instead of simply jki; qji ¼ c k ðr 1 Þc q ðr 2 Þjiji does not change the sum (1) because the bosonic creation (annihilation) operatorsâ þ ki andâ þ qj (â ki andâ qj ) with i Þ j obviously commute. The interaction strength of the pseudopotential Vðr 2 À r 1 Þ ¼ ðr 2 À r 1 Þ has the eigenvalues s or t corresponding to the spin states je s i or je t i of the atomic pair. As such, the potential is nearly independent of nuclear spins: he t n s jje t n s i ¼ he t n t jje t n t i ¼ t and he s n t jje s n t i ¼ he s n s jje s n s i ¼ s (here we write only the spin parts of the matrix elements). Instead, Ahokas et al. used he t n s jje t n s i ¼ he s n t jje s n t i ¼ 0, arguing that the antisymmetric states do not scatter via s waves. This zeroing is only valid if the matrix elements include the vanishing spatial factor hR À jðr 2 À r 1 ÞjR À i. Actually, it is this spatial factor which cancels the contribution of the antisymmetric states to s-wave scattering and to the interaction energy (1). On the contrary, the spatial part of the matrix elements for the symmetric states R þ jiji þ is doubled. In other words, the atoms of a heterostate symmetric pair behave as identical. Clearly, jabi þ ¼ je t n t;0 i and jaci þ ¼ jbdi þ ¼ 1 ffiffi 2 p ðje t;0 n t;0 i þ je s n s iÞ. Consequently, þ ab habjjabi þ ¼ t and þ ac ¼ þ bd ¼ 1 2 ð s þ t Þ. Then, ...

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“…where n is the 2D density of adsorbed H atoms and l ∼ 0.5 nm is their out-of-plane delocalization length in the adsorption potential so that n/l stands in place of the 3D density in Eqs. (1); ∆a = a s − a t = −30 (10) pm [4,14] is the experimental difference between the singlet and triplet scattering length of two ground-state hydrogen atoms (to be compared with the theoretical values ranging from −42 to −55 pm [15,16,17]). The amplitude of the respective modulation of the resonance field in 2D atomic hydrogen at zero detuning (θ ab = π 2 ) is very large, ∆H c = 1.5(5) • 10 −18 G•cm 3 .…”

Section: Endor In Atomic Hydrogenmentioning

confidence: 99%

Interaction-enhanced double resonance in cold gases

2011

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A new type of double-resonance spectroscopy of a quantum gas based on interaction-induced frequency modulation of a probe transition has been considered. Interstate interaction of multilevel atoms causes a coherence-dependent collisional shift of the transition between the atomic states |1 and |2 due to a nonzero population of the state |3 . Thus, the frequency of the probe transition |1 − |2 experiences oscillations associated with the Rabi oscillations between the states |1 and |3 under continuous excitation of the drive resonance |1 − |3 . Such a dynamic frequency shift leads to a change in the electromagnetic absorption at the probe frequency and, consequently, greatly enhances the sensitivity of double-resonance spectroscopy as compared to traditional "hole burning", which is solely due to a decrease in the population of the initial state |1 . In particular, it has been shown that the resonance linewidth is determined by the magnitude of the contact shift and the amplitude of the drive field and does not depend on the static field gradient. The calculated line shape and width agree with the low-temperature electron-nuclear doubleresonance spectra of two-dimensional atomic hydrogen.

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Cold hydrogen-hydrogen scattering using CCA model

Cited by 8 publications

References 37 publications

Clock Shift in High Field Magnetic Resonance of Atomic Hydrogen

Clock Shift in High Field Magnetic Resonance of Atomic Hydrogen

Comment on “Clock Shift in High Field Magnetic Resonance of Atomic Hydrogen”

Interaction-enhanced double resonance in cold gases

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