Re: [BLAST_ANAWARE] target geometry

From: Hauke Kolster (hauke@lns.mit.edu)
Date: Thu Dec 05 2002 - 01:13:42 EST


Hi everybody.
I have gone though the numbers for the target once more. The following
numbers
are an estimate for the ABS and unpol target thicknesses based on the
present and
past cell geometries and the measurements we did on the ABS in the past
weeks.

- unpol H2 into unplugged cell (short injection tube)
0.2 sccm H2 (molecules: 1 atom = 2 nucleons)
cell temperature 300K
cell dimensions:
        L_cell = 400mm, d_cell = 15mm
        L_inj = 40mm, d_inj=10mm (short injection tube)
total conductance: 24.5 l/s
nucleon density in center: 3.32x10^12 nucl/cm^3
average target thickness: 1.33x10^14 nucl.cm^2

- pol H1 into target cell (long injection tube)
injected flux: 1.9x10^16 at/s
cell temperature 100K
cell dimensions:
        L_cell = 400mm, d_cell = 15mm
        L_inj = 130mm, d_inj=10mm (long injection tube)
total conductance: 15.8 l/s
nucleon density in center: 1.22x10^12 nucl/cm^3
average target thickness: 2.43x10^13 nucl.cm^2
This is for a pure atomic target.

Some Comments about target thickness and recombination in case we
recombine a lot in the cell:

Any recombination in the target cell will increase the target
thickness and
might lower the average polarization of the target. The relation between
recombination (a = degree of dissociation) and target density is given
by the
following relations:
The degree of dissociation is defined as

        a = n_1 / [ n_1 + n_2 ]

where n_1 is the number of nucleons in atoms and n_2 is the number of
nucleons in molecules. The conductance of the target cell depends on the
mass of the particle and the densities of nucleons in atoms and
molecules
differs by a factor of sqrt(2). The degree of dissociation in the cell
a_t is then

        a_t = n_1 / [ n_1 + sqrt(2) * n_2 ]

The gain k in total target density relative to a pure atomic target is
expressed
by
        k = sqrt(2) - [ sqrt(2) - 1 ] * a_t

and k between 1 and sqrt(2). The average polarization of the target is

        P_t = a_t * P_a + ( 1 - a_t ) * P_m

where P_a is the polarization of the atoms and P_m is the polarization
of the molecules.

One more comment about terminology. The term dilution does not apply to
an
internal gas target as long as no other species other than the target
gas are
present. Recombination might change the target polarization but it does
not
dilute the target.

Hauke



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