# Deuteron Properties

Here are files with properties of the deuteron for multiple NN potentials.
These include binding energy, D-state %, quadrupole and magnetic moments in impulse approximation, asymptotic D/S ratio, rms and rmq radii.
Also breakdown of the energy into kinetic and potential parts, and various components of the potential.
Following are tables of the wave function in configuration space out to 100 fm, and in momentum space to 20 fm-1.
At the end of each file are the electromagnetic form factors gc, gm, gq and the deuteron structure functions A, B, and t20 (at 70 deg).
These have all been calculated in impulse approximation.
In between we give the relevant wave function integrals ce, cl, cs, and cq, and Kelly nucleon form factors ges and gms used to produce the structure functions.

ce(q)=Integral{ j0(qr)*(u(r)**2+w(r)**2) dr }
cl(q)=Integral{ (j0(qr)+j2(qr))*1.5*w(r)**2 dr }
cs(q)=Integral{ j0(qr)*(u(r)**2-.5*w(r)**2) + j2(qr)*(sqrt(1/2)*u(r)*w(r)+.5*w(r)**2) dr }
cq(q)=Integral{ j2(qr)*(3.*sqrt(1/2)*u(r)*w(r)-.75*w(r)**2)/q**2 dr }

mdeut=mn+mp-ebind
mr=2*mn*mp/(mn+mp)
gc(q)=2.*ges*ce(q)
gm(q)=(mdeut/mr)*(ges*cl(q)+2.*gms*cs(q))
gq(q)=2.*ges*cq(q)

tau=q**2/(2*mdeut/hc)**2
A(q)=gc(q)**2+(8/9)*(tau*gq(q))**2+(2/3)*tau*gm(q)**2
B(q)=(4/3)*tau*(1.+tau)*gm(q)**2
theta=(70/90)*pi/2 ! theta=70 deg
x=(2/3)*tau*gq(q)/gc(q)
y=(1/3)*tau*(gm(q)/gc(q))**2*(1+2*(1+tau)*tan(theta/2)**2)
t20(q)=-sqrt(2)*(x*(x+2)+.5*y)/(1+2*(x**2+y))

Relevant references include the following:

Local Phenomenological Nucleon-Nucleon Potentials
R. V. Reid, Jr.
Ann. Phys. 50, 411 (1968)

Construction d'un potentiel nucléon-nucléon à coeur très mou (SSC)
R. De Tourreil and D. W. L. Sprung
Nucl. Phys. A201, 193 (1973)

Phenomenological two-nucleon interaction operator
I. E. Lagaris and V. R. Pandharipande
Nucl. Phys. A 359, 331 (1981)

Nucleon-nucleon potentials with and without Δ( 1232) degrees of freedom
R. B. Wiringa, R. A. Smith, and T. L. Ainsworth
Phys. Rev. C 29, 1207 (1984)

Accurate nucleon-nucleon potential with charge-independence breaking
R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla
Phys. Rev. C 51, 38 (1995)

Local chiral potentials with Δ-intermediate states and the structure of light nuclei
M. Piarulli, L. Girlanda, R. Schiavilla, A. Kievsky, A. Lovato, L. E. Marcucci, Steven C. Pieper, M. Viviani, and R. B. Wiringa
Phys. Rev. C 94, 054007 (2016)

Local position-space two-nucleon potentials from leading to fourth order of chiral effective field theory
S. K. Saha, D. R. Entem, R. Machleidt, Y. Nosyk
arXiv.2209.13170

Reid Soft Core

Robert B. Wiringa
Last update October 5, 2022