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The wave function of a spheroidal harmonic oscillator without spin-orbit interaction is expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained function of the main quantum numbers and potential derivative. They may be used to test complex computer codes one should develop in a realistic approach of the fission dynamics. The results given for the 240 Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed.
The branching fraction of D+→K0Sπ0e+νe is measured for the first time using 7.93 fb−1 of e+e− annihilation data collected at the center-of-mass energy s√=3.773~GeV with the BESIII detector operating at the BEPCII collider, and is determined to be B(D+→K0Sπ0e+νe) = (0.881 ± 0.017stat. ± 0.016syst.)\%. Based on an analysis of the D+→K0Sπ0e+νe decay dynamics, we observe the S-wave and P-wave components with fractions of fS-wave = (6.13 ± 0.27stat. ± 0.30syst.)% and fK¯∗(892)0 = (93.88 ± 0.27stat. ± 0.29syst.)\%, respectively. From these results, we obtain the branching fractions B(D+→(K0Sπ0)S-wave e+νe) = (5.41 ± 0.35stat. ± 0.37syst.)×10−4 and B(D+→K¯∗(892)0e+νe) = (4.97 ± 0.11stat. ± 0.12syst.)\%. In addition, the hadronic form-factor ratios of D+→K¯∗(892)0e+νe at q2=0, assuming a single-pole dominance parameterization, are determined to be rV=V(0)A1(0)=1.43 ± 0.07stat. ± 0.03syst. and r2=A2(0)A1(0)=0.72 ± 0.06stat. ± 0.02syst.
Charged-particle spectra at midrapidity are measured in Pb-Pb collisions at the centre-of-mass energy per nucleon-nucleon pair sNN−−−√ = 5.02 TeV and presented in centrality classes ranging from most central (0-5%) to most peripheral (95-100%) collisions. Possible medium effects are quantified using the nuclear modification factor (RAA) by comparing the measured spectra with those from proton-proton collisions, scaled by the number of independent nucleon-nucleon collisions obtained from a Glauber model. At large transverse momenta (8<pT<20 GeV/c), the average RAA is found to increase from about 0.15 in 0-5% central to a maximum value of about 0.8 in 75-85% peripheral collisions, beyond which it falls off strongly to below 0.2 for the most peripheral collisions. Furthermore, RAA initially exhibits a positive slope as a function of pT in the 8-20 GeV/c interval, while for collisions beyond the 80% class the slope is negative. To reduce uncertainties related to event selection and normalization, we also provide the ratio of RAA in adjacent centrality intervals. Our results in peripheral collisions are consistent with a PYTHIA-based model without nuclear modification, demonstrating that biases caused by the event selection and collision geometry can lead to the apparent suppression in peripheral collisions. This explains the unintuitive observation that RAA is below unity in peripheral Pb-Pb, but equal to unity in minimum-bias p-Pb collisions despite similar charged-particle multiplicities.
Charged-particle spectra at midrapidity are measured in Pb-Pb collisions at the centre-of-mass energy per nucleon-nucleon pair sNN−−−√ = 5.02 TeV and presented in centrality classes ranging from most central (0-5%) to most peripheral (95-100%) collisions. Possible medium effects are quantified using the nuclear modification factor (RAA) by comparing the measured spectra with those from proton-proton collisions, scaled by the number of independent nucleon-nucleon collisions obtained from a Glauber model. At large transverse momenta (8<pT<20 GeV/c), the average RAA is found to increase from about 0.15 in 0-5% central to a maximum value of about 0.8 in 75-85% peripheral collisions, beyond which it falls off strongly to below 0.2 for the most peripheral collisions. Furthermore, RAA initially exhibits a positive slope as a function of pT in the 8-20 GeV/c interval, while for collisions beyond the 80% class the slope is negative. To reduce uncertainties related to event selection and normalization, we also provide the ratio of RAA in adjacent centrality intervals. Our results in peripheral collisions are consistent with a PYTHIA-based model without nuclear modification, demonstrating that biases caused by the event selection and collision geometry can lead to the apparent suppression in peripheral collisions. This explains the unintuitive observation that RAA is below unity in peripheral Pb-Pb, but equal to unity in minimum-bias p-Pb collisions despite similar charged-particle multiplicities.
We introduce a transport approach which combines partonic and hadronic degrees of freedom on an equal footing and discuss the resulting reaction dynamics. The initial parton dynamics is modeled in the framework of the parton cascade model, hadronization is performed via a cluster hadronization model and configuration space coalescence, and the hadronic phase is described by a microscopic hadronic transport approach. The resulting reaction dynamics indicates a strong influence of hadronic rescattering on the space-time pattern of hadronic freeze-out and on the shape of transverse mass spectra. Freeze-out times and transverse radii increase by factors of 2 3 depending on the hadron species.
Using e+e− annihilation data corresponding to an integrated luminosity of 2.93 fb−1 taken at the center-of-mass energy s√=3.773~GeV with the BESIII detector, a joint amplitude analysis is performed on the decays D0→π+π−π+π− and D0→π+π−π0π0(non-η). The fit fractions of individual components are obtained, and large interferences among the dominant components of D0→a1(1260)π, D0→π(1300)π, D0→ρ(770)ρ(770) and D0→2(ππ)S are found in both channels. With the obtained amplitude model, the CP-even fractions of D0→π+π−π+π− and D0→π+π−π0π0(non-η) are determined to be (75.2±1.1stat.±1.5syst.)% and (68.9±1.5stat.±2.4syst.)%, respectively. The branching fractions of D0→π+π−π+π− and D0→π+π−π0π0(non-η) are measured to be (0.688±0.010stat.±0.010syst.)% and (0.951±0.025stat.±0.021syst.)%, respectively. The amplitude analysis provides an important model for binning strategy in the measurements of the strong phase parameters of D0→4π when used to determine the CKM angle γ(ϕ3) via the B−→DK− decay.
Using e+e− annihilation data corresponding to an integrated luminosity of 2.93 fb−1 taken at the center-of-mass energy s√=3.773~GeV with the BESIII detector, a joint amplitude analysis is performed on the decays D0→π+π−π+π− and D0→π+π−π0π0(non-η). The fit fractions of individual components are obtained, and large interferences among the dominant components of D0→a1(1260)π, D0→π(1300)π, D0→ρ(770)ρ(770) and D0→2(ππ)S are found in both channels. With the obtained amplitude model, the CP-even fractions of D0→π+π−π+π− and D0→π+π−π0π0(non-η) are determined to be (75.2±1.1stat.±1.5syst.)% and (68.9±1.5stat.±2.4syst.)%, respectively. The branching fractions of D0→π+π−π+π− and D0→π+π−π0π0(non-η) are measured to be (0.688±0.010stat.±0.010syst.)% and (0.951±0.025stat.±0.021syst.)%, respectively. The amplitude analysis provides an important model for binning strategy in the measurements of the strong phase parameters of D0→4π when used to determine the CKM angle γ(ϕ3) via the B−→DK− decay.
Utilizing the data set corresponding to an integrated luminosity of 3.19 fb−1 collected by the BESIII detector at a center-of-mass energy of 4.178 GeV, we perform an amplitude analysis of the D+s→π+π−π+ decay. The sample contains 13,797 candidate events with a signal purity of ∼80%. We use a quasi-model-independent approach to measure the magnitude and phase of the D+s→π+π−π+ decay, where the P and D waves are parameterized by a sum of three Breit-Wigner amplitudes ρ(770)0, ρ(1450)0, and f2(1270). The fit fractions of different decay channels are also reported.
Utilizing the data set corresponding to an integrated luminosity of 3.19 fb−1 collected by the BESIII detector at a center-of-mass energy of 4.178 GeV, we perform an amplitude analysis of the D+s→π+π−π+ decay. The sample contains 13,797 candidates with a signal purity of ∼80%. The amplitude and phase of the contributing ππ S wave are measured based on a quasi-model-independent approach, along with the amplitudes and phases of the P and D waves parametrized by Breit-Wigner models. The fit fractions of different intermediate decay channels are also reported.
We report an amplitude analysis and branching fraction measurement of D+s→K+K−π+ decay using a data sample of 3.19 fb−1 recorded with BESIII detector at a center-of-mass energy of 4.178 GeV.
We perform a model-independent partial wave analysis in the low K+K− mass region to determine the K+K− S-wave lineshape, followed by an amplitude analysis of our very pure high-statistics sample.
The amplitude analysis provides an accurate determination of the detection efficiency allowing us to measure the branching fraction B(D+s→K+K−π+)=(5.47±0.08stat±0.13sys)%.