1. Accurate analytic potentials for BeH, BeD & BeT
Nike Dattani & Staszek Welsh
Oxford University & Kyoto University　　
2014年 6月 20日

2. Best ab initio for Li2 (6e-)
Recent experiments needed +/ cm-1 predictions 
Experiment would take several years, need better than ab initio

3. Alternative to ab initio : Empirical potential (MLR)
Using very little data,
All energies can be predicted very accurately

4. Experiment successful BECAUSE,
MLR’s predicted energies were much better than ab initio
Used 1000 digits for maple calculation

5. MLR (Morse / Long-Range) Potential
It’s a Morse potential,
but with the correct long-range built in !!!

6. MLR (Morse / Long-Range) Potential
for large r, we should have for HeH+:
V(r) = De – C4 / r4 – C6 / r6 – C7 / r7 – C8 / r8 … So
u(r) = C4 / r4 + C6 / r6 + C7 / r7 + C8 / r8 …
It’s a Morse potential,
but we can make the long-range part correct !!!

7. V(r) = De – C4 / r4 – C6 / r6 – C7 / r7 – C8 / r8 …
C4 : dipole polarizability
C6 : quadrupole polarizability, non-adiabatic dipole polarizability
C7 : mixed dipole-dipole-quadrupole polarizability (3rd order)
C8 : hyperpolarizability (4th order), octupole polarizability,
& non-adiabatic quadrupole polarizability

8. for large r, we should have:
V(r) = De – C4 / r4 – C6 / r6 – C7 / r7 – C8 / r8 …
C4 : dipole polarizability
non-relativistic
(1)
13 digits !
relativistic corrections
-80.35(2)
QED 3rd order modulo Bethe ln
QED 3rd order with Bethe ln
QED 4th order, finite-mass 3rd order
30.473(1)
0.193(2)
0.49(23)
total dipole polarizability
(23)

9. for large r, we should have:
V(r) = De – C4 / r4 – C6 / r6 – C7 / r7 – C8 / r8 …
C6 : quadrupole polarizability
non-relativistic
(5)
12 digits !!!
relativistic corrections
(2) x 10-4
finite-mass corrections
(3) x 10-3
total quadrupole polarizability
(4)

10. 1e- : Mu  : H  2e- : He : H2 3e- : Li 2e- : HeH+ In Progress
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4

11. 1e- : Mu  : H  2e- : He : H2 3e- : Li 5e- : BeH
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4

12. 5e- : BeH V(r) = - C6 / r3 – C8 / r6 – C10 / r8 …
Most accurate empirical potential:
2006 Le Roy et al. JMS 236,
 C6, C8, C10 not included
 couldn’t determine leading BOB term (u0 )
 De had uncertainty of +/- 200cm-1
 single-state fit (excited states not included)
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4

13. Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4

14. 5e- : BeH    Next step!  C6, C8, C10 not included
 couldn’t determine leading BOB term (u0 )
 De had uncertainty of +/- 200cm-1
 single-state fit (excited states not included)  
Next step!
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4

15. 1e- : Mu 2e- : He : H2 3e- : Li 5e- : BeH in progress 5e- : LiHe
Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4

16. Experimental energy gap is hyperfine structure according to table 4 of:
He (from Table VIII of Experimental: (16)
Theoretical:
Fourth order means: alpha^4

17. Thank you 
VERY MUCH !!!