We report a set of measurements of particle production in inelastic pp collisions collected with a minimum-bias trigger at the Tevatron Collider with the CDF II experiment. The inclusive charged particle transverse momentum differential cross section is measured, with improved precision, over a range about ten times wider than in previous measurements. The former modeling of the spectrum appears to be incompatible with the high particle momenta observed. The dependence of the charged particle transverse momentum on the event particle multiplicity is analyzed to study the various components of hadron interactions. This is one of the observable variables most poorly reproduced by the available Monte Carlo generators. A first measurement of the event transverse energy sum differential cross section is also reported. A comparison with a pythia prediction at the hadron level is performed. The inclusive charged particle differential production cross section is fairly well reproduced only in the transverse momentum range available from previous measurements. At higher momentum the agreement is poor. The transverse energy sum is poorly reproduced over the whole spectrum. The dependence of the charged particle transverse momentum on the particle multiplicity needs the introduction of more sophisticated particle production mechanisms, such as multiple parton interactions, in order to be better explained.
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.
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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