function wn(xn,a,ane,z)
c
c     evaluation of the occupation probablities for a hydrogenic ion
c     using eqs (4.26), and (4.39) of Hummer,Mihalas Ap.J. 331, 794, 1988.
c     approximate evaluation of Q(beta) - Hummer
c
c     Input: xn  - real number corresponding to quantum number n
c            a   - correlation parameter
c            ane - electron density
c            z   - ionic charge
c
      INCLUDE 'IMPLIC.FOR'
      INCLUDE 'BASICS.FOR'
      parameter (p1=0.1402,p2=0.1285,p3=un,p4=3.15,p5=4.)
      parameter (tkn=3.01,ckn=5.33333333,cb0=8.59d14)
      parameter (f23=-2./3.)
c
      cb=cb0*bergfc
c
c     evaluation of k(n)
c
      if(xn.le.tkn) then
         xkn=un
       else
         xn1=un/(xn+un)
         xkn=ckn*xn*xn1*xn1
      end if
c
c     evaluation of beta
c
      beta=cb*z*z*z*xkn/(xn*xn*xn*xn)*exp(f23*log(ane))
c
c     approximate expression for Q(beta)
c
      x=exp(p4*log(un+p3*a))
      c1=p1*(x+p5*(z-un)*a*a*a)
      c2=p2*x
      f=(c1*beta*beta*beta)/(un+c2*beta*sqrt(beta))
      wn=f/(un+f)
      return
      end