Radius and radial moments of the deuteron

Abstract

New values are extracted for the deuteron rms matter radius rD =1.9547+0.0019 fm and the matter radial deuteron moments ( r ) = 54. 2+0. 1 fm and ( r6) = 1828+1 fm6 by analyzing the experimental ratio of (e, d) to (e,p) scattering.PACS number(s): 21.45.+v, 21.10.Ft, 25.30.8f, 27.10.+h Qk= ( )k 2k (2k +1)! (2b) The "experimental" values of CE(q ) are obtained from the experimental data of Simon et al. [3] for the ratio R(q )=GzD(q )/Gz (q ) of deuteron to proton form factors by using CE(q )=R(q )(1+x)'~[ 1+GE"(q )/GE&(q )] and the relationof Isgur et al. [8], where Gz"(q ) is the neutron form factor, r = q /4m is the Darwin-Foldy correction, and m =938.2786/Ac=4. 57491 fm ' is the proton mass.The expansion of CE(q ) in powers of q may be written for the present purpose in the form n=N There is increasing interest in the literature [1 -7] in extracting the deuteron matter radius r D by analyzing results of elastic electron scattering experiments. Some of these analyses, and also the analysis of this paper, involve fitting the "experimental" electric charge form factor CE(q ) in the low-q region by a polynomial of a certain order in q [5]; CE(q )=1+a, q +a2q + where r D = 6a, orequally wellby using a continued-fraction method [6]. We recall that the matter radial moment (r ") is the expectation value of (r/2) ":The coefficients ak are related to the radial moments ( r ")thy correct asymptotic behavior, i.e. , fitting the recent experimental values of the asymptotic S-state amplitude As=0. 8838+0.0004 fm '~o f Stoks et al. [9] and the asymptotic D /S ratio g =0.0273+0.0005 of Borbely et al. [10]. The value g = 0.0273+0.0005 of Borbely et al. [10] is consistent, in particular, with our recent prediction g=0.02701+0.00019 [11]. The MHKZ potential fits too the experimental value of the deuteron quadrupole moment (Q = 0.2860+0.0015 fm [12] and Q =0.2859+0.0003 fm [13]). Unfortunately, the values listed in Table I of Ref. [7] for the free parameters of this potential are overtruncated; therefore, they are given here in Table I with a larger number of significant figures.The values assumed for m are m =2, 3, 4, and 5 and for X is X =70. The meson exchange current (MEC) contribution is taken into account by using the correction b, rD =0.0034+0.0003 fm of Kohno [14].To make the values of ak of Eqs. (1) and (5) more consistent with the values of Cz(q ) (and hence, more accurate results would have been obtained), the point Cz(0) = 1 given by the boundary condition is used as a constraint and the analytic asymptotic contribution e= f z(u +w )dr to the normalization factor [Jo"(u +to )dr] '~i s neglected by the numerical methods producing the deuteron waves u and w of the local potential MHKZ of Ref. [7]. Deuteron properties, in particular Az and q, will not change by neglecting e, except for rD, ' it negligibly changes from 1.96316 fm to 1.96256 fm. A small change in rD would not aftect the results of the analysis (as discussed in conjunction with Table III).The results of fitting the experimental data are listed in ...

Meson and Quark Degrees of Freedom and the Radius of the Deuteron

“…( 5) and given in column 1. To calculate r ch from the matter radii r m [1,9,20,21,22] we use r p = 0.862 (12) fm, the neutron charge radius of the respective references, the standard Darwin-Foldy contribution, r 2 DF = 0.0331 fm 2 , the spin-orbit correction for the Paris potential r 2 SO = −0.0015 fm 2 , and the non-nucleonic contribution r 2…”

“…The first five entries in column 2 are the results of various analyses [1,9,20,21,22] of elastic electron scattering data [12,15] aiming at the matter radius r m . The non-nucleonic correction r 2 [2] used in these analyses is based on π-meson exchange only; it is listed in column 3.…”

“…(5) and given in column 1. To calculate r ch from the matter radii r m [1,9,20,21,22] we use r p = 0.862(12) fm, the neutron charge radius of the respective references, the standard Darwin-Foldy contribution, r 2 DF = 0.0331 fm 2 , the spin-orbit correction for the Paris potential r 2 SO = −0.0015 fm 2 , and the non-nucleonic contribution r 2 [2] of column 3. In the last two rows the deuteron charge and matter radii are calculated from the experimental charge radius difference (r 2 ch − r 2 p ) exp = 3.795(19) fm 2 [14] and (r 2 ch − r 2 p ) exp = 3.807(26) fm 2 [23] as determined by the isotope shift of the 1s − 2s transition in atomic hydrogen.…”

Untitled

“…where j 0 and j 2 are the spherical Bessel functions of order zero and two, respectively. The factor τ = (q 2 /4m 2 p ) is called the Darwin-Foldy correction to the nucleon form factors [22], where m p = 4.5749098 fm −1 is the proton mass. Note that, Eq.…”

Untitled

“…In each case, the binding energy of the deuteron is E b = −2.224644MeV . The number of nodes in the radial deuteron wave functions is N. (a) [11]; (b) [12]; (d) [13]; (c) [14,15]; (e) [16]. short-range repulsion caused by the hard-core is relatively large.…”