# Formation processes and secondary emission coefficients for H/sup -/ production on alkali-coated surfaces Page: 4 of 7

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? = r + z,

n = r - z,

4> = <J>.

(5)

Upon setting the azimuthal quantum number equal to

zero, expressing lengths and energies in units of

Bohr radii and Rydbergs, respectively, and des-

cribing the negative ion by a coulomb state with

effective charge Z and unperturbed energy level

equal to Z2, the introduction of coordinates (5)

into eq. (1) leads to an n equation

^tijw+Vo+VI+Stye,+?_L_jv,o.

(6)

The term V0 in the brackets is a uniform potential

within the substrate; the term VI is a constant

term equal to the surface work function and

applicable in certain regions (see figs. 3 and 5);

the next two terms arise from the coulomb term

and coordinate choice, respectively; the term with

electric field coefficient occurs in those

regions of uniform electric field; the last term

in the brackets is the image term, with zQ the

z-coordinate of the imqe plane measured from the

center of the negative ion. The separation of

coordinates fails only in the case of the image

term which contains the c coordinate explicitly.

As Janev was the first to point out, £ « n in

the range of integration, and by neglecting this

coordinate in the image term we have effectively

achieved a separation.

The function v(n) is complex. Writing

v = u + iw and introducing into equation (6), we

obtain a pair of coupled equations for the real

and imaginary functions of v ;

A

dn2

d^w

dn2

■f(£ + VI+T*7+-n'

■1|E + VI + 1,Z' +Vfcn‘

_l_

n +2z0

1_

n + ?z0

We are interested in a solution of Eqs. (7) which

represents a standing wave negative ion function

in the negative ion region and a purely outgoing

wave propagating in the region of the wefa? sub-

strate. Referring to Eq. (6), within the sub-

strate this equation reduces to

d£v

dn2

0.

(8)

with solution

Equation (9) has the form required for a purely

outgoing wave. Matching this solution to the

interior solutions for u and w at the boundary of

the substrate, the matching conditions become

u*u + w*w

Uz + wz

i [PHPP/]'

uw1 - wu*

1

ft

ip) *>l p)! * «f

do)

The integration procedure consists of select-

ing a negative ion separation distance Zp, and

searching for values of E and r which satisfy the

conditions (10), The resulting value for r gives

the transition rate, r/TT, at that separation

distance. The rate of loss of electron density

is, from (4),

=. i m2

dt tr m •

(ID

the loss rate T/Tf is a function of separation

distance z0; writing dt = dz0/v, where v is the H”

ion velocity as it moves away from the surface,

the fraction of H~ ions surviving the electron

loss to the substrate becomes

-3-

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Hiskes, J.R. & Karo, A. Formation processes and secondary emission coefficients for H/sup -/ production on alkali-coated surfaces, article, September 20, 1977; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc1074337/m1/4/: accessed January 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.