Improved calculation of the muonic-helium Lamb shift

Proton radii ofHe4,6,8isotopes from high-precision nucleon-nucleon interactions

“…Another comment concerning the difficulty of performing the NCSM calculations is that the matrices become less sparse when the number of particles decrease. To keep the comparison with the standard shell model, in 4 He we have a dimension 12.5 smaller than in 56 Ni but 1.5 times more non-zero matrix elements. For all these reasons, NCSM calculations with large N max model spaces are difficult but still feasible with a computer with a large RAM memory and a large disk capacity.…”

“…A similar experiment for 8 He is under way. We have performed large-scale ab initio calculations for 4,6,8 He isotopes using highprecision nucleon-nucleon (NN) interactions within the no-core shell model (NCSM) approach. With the CD-Bonn 2000 NN potential we found point-proton root-mean-square (rms) radii of 4 He and 6 He 1.45(1) fm and 1.89(4), respectively, in agreement with experiment and predict the 8 He point proton rms radius to be 1.88(6) fm.…”

“…Precision laser spectroscopy on individual 6 He atoms confined and cooled in a magneto-optical trap was performed and measured the isotope shift between 6 He and 4 He. With the help of precise quantum mechanical calculations with relativistic and QED corrections [3] and from the knowledge of the charge radius of 4 He (1.673(1) [4]), it was possible to determine the charge radius of 6 He to be 2.054 ± 0.014 fm [2]. The large difference between the 4 He and 6 He charge radii is due to the extra two loosely bound neutrons in 6 He that form a halo [5].…”

The 4He total photo-absorption cross section with two- plus three-nucleon interactions from chiral effective field theory

“…As we Table 1 Calculated 4 He ground-state energy E 0 , point-proton root-meansquare radius r 2 p 1 2 , and total dipole strength Ψ 0 |D †D |Ψ 0 obtained using the χEFT NN and NN+NNN interactions compared to experiment. The experimental value of the point-proton radius is deduced from the measured alpha-particle charge radius, r 2 c 1 2 = 1.673(1) fm [32], proton charge radius, R 2 p 1 2 = 0.895(18) fm [33], and neutron mean-square-charge radius, R 2 n = −0.120 (5) will see later, this also implies rather weak NNN effects on the 4 He photo-absorption cross section at low energy.…”

Lamb shift in muonic ions of lithium, beryllium, and boron

“…Fundamentals of calculating of energy spectra for light muonic atoms were formulated many years ago in relativistic approach based on the Dirac equation, and in nonrelativistic Schrödinger method in [11][12][13][14][15][16] (see other references in review articles [13,15]). After recent experiments of the CREMA collaboration in 2010 year there were many works devoted to the muonic atoms, in order to overcome the arisen difference in the magnitude of the charge radius of the proton [17][18][19][20][21][22][23][24][25][26] (see other references in [3]).…”