Component Manual for the Neutron Ray-Tracing Package McStas, version 3.8.6

9.2  The Tunneling_sample McStas Component

A Double-cylinder shaped all-incoherent scatterer with elastic, quasielastic (Lorentzian), and tunneling (sharp) components.

Identification

Description

A Double-cylinder shaped all-incoherent scatterer with both elastic, quasielastic (Lorentzian), and tunneling (sharp) components. No multiple scattering. Absorbtion included. The shape of the sample may be a box with dimensions xwidth, yheight, zdepth. The area to scatter to is a disk of radius ’focus_r’ situated at the target. This target area may also be rectangular if specified focus_xw and focus_yh or focus_aw and focus_ah, respectively in meters and degrees. The target itself is either situated according to given coordinates (x,y,z), or defined with the relative target_index of the component to focus to (next is +1). This target position will be set to its AT position. When targeting to centered components, such as spheres or cylinders, define an Arm component where to focus to.

The outgoing polarization is calculated as for nuclear spin incoherence:

P’ = 1/3*P-2/3P = -1/3P

As above multiple scattering is ignored .

Example: Tunneling_sample(thickness=0.001,radius=0.01,yheight=0.02,focus_r=0.035, target_index=1)

Input parameters

Parameters in boldface are required; the others are optional.

Name

Unit

Description

Default

thickness

m

Thickness of cylindrical sample in (x,z) plane

0

radius

m

Outer radius of sample in (x,z) plane

0.01

focus_r

m

Radius of disk containing target. Use 0 for full space

0

p_interact

1

MC Probability for scattering the ray; otherwise transmit

1

f_QE

1

Fraction of quasielastic scattering

0

f_tun

1

Fraction of tunneling scattering (f_QE+f_tun < 1)

0

gamma

meV

Lorentzian width of quasielastic broadening (HWHM)

0

E_tun

meV

Tunneling energy

0

target_x

m

X-position of target to focus at

0

target_y

m

Y-position of target to focus at

0

target_z

m

Z-position of target to focus at

0.235

focus_xw

m

horiz. dimension of a rectangular area

0

focus_yh

m

vert. dimension of a rectangular area

0

focus_aw

deg

horiz. angular dimension of a rectangular area

0

focus_ah

deg

vert. angular dimension of a rectangular area

0

xwidth

m

horiz. dimension of sample, as a width

0

yheight

m

vert. dimension of sample, as a height

0.05

zdepth

m

depth of sample

0

sigma_abs

barns

Absorbtion cross section pr. unit cell

5.08

sigma_inc

barns

Total incoherent scattering cross section pr. unit cell

4.935

Vc

Å\(^{3}\)

Unit cell volume

13.827

target_index

1

relative index of component to focus at, e.g. next is +1

0

Links

An incoherent inelastic scatterer

The component Tunneling_sample displays incoherent inelastic scattering as found in a number of systems, e.g. containing mobile hydrogen.

For the sample geometry, we default use a hollow cylinder (which has the solid cylinder as a limiting case). The sample dimensions are: Inner radius \(r_\textrm {i}\), outer radius \(r_\textrm {o}\), and height \(h\). This geometry is the same as the default for V_sample, see figure 9.2.

As for V_sample, the sample geometry can be made rectangular by specifying the width, \(w_x\), the height, \(h_y\), and the thickness, \(t_z\).

Also the focusing properties are the same as for V_sample. For the focusing is performed as a uniform distribution on a target sphere of radius \(r_\textrm {foc}\), at the position \((x_\textrm {target},y_\textrm {target},z_\textrm {target})\) in the local coordinate system. The focusing can alternatively be performed on a rectangle with dimensions \(w_\textrm {focus}\), \(h_\textrm {focus}\), or uniformly in angular space (in a small-angle approximation), using \(w_\textrm {foc, angle}\), \(h_\textrm {foc, angle}\). The focusing location can be picked to be a downstream component by specifying target_index.

The incoherent and absorption cross sections for V are default for the component. For other choices, the parameters \(\sigma _\textrm {inc}\), \(\sigma _\textrm {abs}\), and the unit cell volume \(V_0\) should be specified. For a loosely packed sample, also the packing factor, \(f_\textrm {pack}\) can be specified (default value of 1).

The inelastic scattering takes place as a quasielastic (Lorentzian) component, which is chosen with probability \(f_\textrm {QE}\). The broadening of the signal is given by \(\Gamma \) (HWHM). In addition, a tunneling signal is present with a probability of \(f_\textrm {tun}\) and a tunneling energy of \(\pm E_\textrm {tun}\). The tunneling peaks are weighted by the usual factor \(k_\textrm {f}/k_\textrm {i}\).

The total scattering cross section is given by

\begin {eqnarray} \lefteqn {\frac {d^2\sigma }{d\Omega dE_\textrm {f}}(q,\omega ) = \frac {\sigma _\textrm {inc}}{4\pi } \times \left \{ (1-f_\textrm {QE}-f_\textrm {inel}) \delta (\hbar \omega ) \right . } \\ &+& f_\textrm {QE} \frac {\Gamma }{(\hbar \omega )^2+\Gamma ^2} + \left .\frac {f_\textrm {inel}}{2} \frac {k_\textrm {f}}{f_\textrm {i}} \left [\delta (\hbar \omega -E_\textrm {tun}) + \delta (\hbar \omega +E_\textrm {tun}) \right ] \right \} \nonumber \end {eqnarray}

The component takes care that \(f_\textrm {QE} + f_\textrm {tun} \leq 1\), otherwise an error is returned.

The component accounts for absorption, but not multiple scattering. To obtain intensities similar to real measured ones, we therefore do not take attenuation from scattering into account for the outgoing neutron ray.