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ELECTRONIC STRUCTURES OF MUONIC ATOMS AND MOLECULES
H. Adachi, T. Mukoyama
To cite this version:
H. Adachi, T. Mukoyama. ELECTRONIC STRUCTURES OF MUONIC ATOMS AND MOLECULES. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-733-C9-736.
�10.1051/jphyscol:19879125�. �jpa-00227234�
JOURNAL DE PHYSIQUE
Colloque C9, supplbment au n012, Tome 48, decembre 1987
ELECTRONIC STRUCTURES OF MUONIC ATOMS AND MOLECULES
H. ADACHI and T. MUKOYAMA"
Hyogo University of Teacher Education, Shimokume, Yashiro-Cho, Kato-Gun, Hyogo 673-14, Japan
"~nstitute for Chemical Research, Kyoto University, Yoshida, Kyoto 606, Japan
Abstract.
-
Electronic structures of muonic atoms and molecules have been calculated for various muonic states. The system of the muon and electrons is treated self-consistently. The Hartree-Fock-Slater method is used for atoms and for molecules the discrete-variational Xa method is applied. The obtained energy eigenvalues and charge distributions of electrons are compared with those of atoms and molecules with 2-1, where Z is the atomic number.When negative muons are stopped in matters, they are in general captured by atomic nuclei to form muonic atoms or molecules. In tlkis case, the interplay between the muon and the atomic electrons is very important. Although there have been reported extensive works on the muonic states in atoms [I], the studies on the electronic states are rather scarce. In the present work, we have calculated the energy and wave functions of muonic atoms and molecules by treating the muon- -electron system self-consistently. For this purpose, we used the Hartree-Fock-Slater (or X a ) method [ 2 ] for atoms and the discrete- -variational Xa (DV-Xa) method [3] for molecules. The effect of the finite nuclear size was taken into account by assuming the nucleus as a uniformly charged sphere.
The muon is usually captured into a high atomic orbit of a
particular atom and cascades down through electron cloud by ejecting Auger electrons from the atom. When the muon is found inside the innermost electron orbit, the muonic atom is generally in a positively
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879125
C9-734 JOURNAL DE PHYSIQUE
Table 1. Comparison of energy eigenvalues (eV) for p - ~ l
+
atom with those of Mg and A1 atoms.muonic state
M9 Is 5 s 5~ 10s 14 s 2 0 s A1
ionized state due to Auger process during the muon cascade. However, it is very difficult to know how many electrons still remain in the atom when the muon is in a particular state. In the present work, we assumed that the atomic vacancies produced by preceeding Auger
transitions are refilled immediately and only an outermost electron is removed.
The calculated electron energy eigenvalues for p-~l' atom are shown in Table 1 for various muonic states and compared with the values for
Table 2. Comparison of electron energy eigenvalues (eV) of V-HL~+ molecule with those of Li atom and LiH molecule.
muonic state
NO+
10sFig. 1. Contours of the electron density of CO molecu1.e and
NO+
molecules for Is, 10s and 14s muonic states.
The difference of the electron density for the muonic molecule from that of the CO molecule, A, is also shown. The solid line represents positive values, while the dashed line indicates negative values.
JOURNAL DE PHYSIQUE
M g and A 1 atoms. A s i m i l a r comparison o f t h e r e s u l t s f o r U - H L ~
+
molecule w i t h t h o s e f o r L i atom and LiH molecule i s l i s t e d i n Table 2.
The muon i s l o c a t e d i n t h e hydrogen atom. I n t h e DV-Xa c a l c u l a t i o n s f o r m o l e c u l e s , t h e s t a t i s t i c a l exchange p a r a m e t e r a i s always t a k e n t o b e 0.7. F o r muonic s t a t e s w i t h s m a l l p r i n c i p a l quantum number n, t h e e n e r g y e i g e n v a l u e s a r e a l m o s t e q u a l t o t h o s e f o r t h e atom w i t h Z - 1 . T h i s f a c t means t h a t t h e muon s c r e e n s a l m o s t c o m p l e t e l y one u n i t o f n u c l e a r c h a r g e . For n = 1 4 , t h e Bohr r a d i u s o f t h e muon o r b i t becomes c l o s e t o t h a t o f t h e i n n e r m o s t e l e c t r o n o r b i t and t h e e n e r g y e i g e n - v a l u e o f t h e 1s e l e c t r o n i s s t r o n g l y i n f l u e n c e d by t h e p r e s e n c e o f t h e muon.
I n F i g . 1, t h e c o n t o u r s o f t h e e l e c t r o n d e n s i t y o f CO molecule and t h e muonic molecule p-NO
+
a r e p l o t t e d f o r v a r i o u s muonic s t a t e s . The muon i s c o n s i d e r e d t o s t a y i n t h e n i t r o g e n s i t e . The d i f f e r e n c e o f t h e e l e c t r o n d e n s i t y o f t h e muonic molecule from t h a t o f t h e CO molecule i s a l s o shown i n t h e f i g u r e . I t i s s e e n t h a t i n t h e muonic molecule t h e e l e c t r o n s a r e more l o c a l i z e d a t t h e oxygen s i t e i n comparison w i t h t h e CO molecule and t h i s e f f e c t i s enhanced w i t h i n c r e a s i n g t h e p r i n c i p a l quantum number o f t h e muonic s t a t e .R e f e r e n c e s
[ l ] B o r i e , E., and Rinker, G.A., Rev. Mod. Phys.
4
(1982) 67.[2] Herman, F., and S k i l l m a n , S . , "Atomic S t r u c t u r e C a l c u l a t i o n s " , ( P r e n t i c e - H a l l , Englewood C l i f f s , N.J.) 1963.
[3] Adachi, H . , Tsukada, M., and Satoko, C., J. Phys. Soc. Jpn
45
(1978) 875.
