Build the FT0 MCP stack and radiator wrap from running planes

This makes the FT0 photocathode reachable by a navigator other than TGeo's and
puts the reflector strips inside their own mother.

- The layer thicknesses are Float_t and each layer's z was summed in a
  different order, so 0MTO and 0REG were 0.075 nm apart and 0REG and 0MCP
  overlapped by 0.24 nm. VecGeom abandoned 0REG with DistanceToOut = -1, so no
  Cherenkov photon was ever registered.
- The stack is now built from one running plane, mirroring the addition the box
  shape uses for its own half-length.
- 0TRE was declared one micron wider than the radiator while each reflector
  strip is four microns thick, so three quarters of every strip lay outside its
  mother. The geometry doctor reports those strips at 23.9 to 27.2 percent
  reachable. The container is now derived from its contents.
- The strips are seated against the radiator in double, closing a 0.33 nm gap.
- Neither change moves the light yield: 41783 +- 564 hits per event before and
  40995 +- 534 after, with the beam aimed into FT0-A.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

Author: sawenzel

Detectors/FIT/FT0/simulation/src/Detector.cxx

@@ -203,10 +203,17 @@ void Detector::SetOneMCP(TGeoVolume* ins)
 
   Double_t x, y, z;
 
-  Float_t ptop[3] = {1.324, 1.324, 1.};      // Cherenkov radiator
-  Float_t ptopref[3] = {1.3241, 1.3241, 1.}; // Cherenkov radiator wrapped with reflector
-  Double_t prfv[3] = {0.0002, 1.323, 1.};    // Vertical refracting layer bettwen radiators and between radiator and not optical Air
-  Double_t prfh[3] = {1.323, 0.0002, 1.};    // Horizontal refracting layer bettwen radiators and ...
+  Float_t ptop[3] = {1.324, 1.324, 1.};   // Cherenkov radiator
+  Double_t prfv[3] = {0.0002, 1.323, 1.}; // Vertical refracting layer bettwen radiators and between radiator and not optical Air
+  Double_t prfh[3] = {1.323, 0.0002, 1.}; // Horizontal refracting layer bettwen radiators and ...
+  // Cherenkov radiator wrapped with reflector. The container has to hold the radiator plus one
+  // reflector strip on each side, so its half-width is the radiator's plus the full strip
+  // thickness. It was written as the radiator plus 1 um while a strip is 4 um thick, which left
+  // each strip sticking 3 um out of its own mother. The clearance keeps the strips off the
+  // container wall, so no daughter face sits exactly on the mother's.
+  const double kWrapClearance = 1.e-4; // cm
+  Float_t ptopref[3] = {static_cast<Float_t>(ptop[0] + 2 * prfv[0] + kWrapClearance),
+                        static_cast<Float_t>(ptop[1] + 2 * prfh[1] + kWrapClearance), 1.};
   Float_t pmcp[3] = {2.949, 2.949, 0.66};    // MCP
   Float_t pmcpinner[3] = {2.749, 2.749, 0.1};
   Float_t pmcpbase[3] = {2.949, 2.949, 0.675};
@@ -231,39 +238,52 @@ void Detector::SetOneMCP(TGeoVolume* ins)
   Int_t ntops = 0, nrfvs = 0, nrfhs = 0;
   x = y = z = 0;
   topref->AddNode(top, 1, new TGeoTranslation(0, 0, 0));
-  float xinv = -ptop[0] - prfv[0];
+  // Each reflector strip has to sit against the radiator with no gap: SetBorderSurface below
+  // makes 0TOP/0RFV and 0TOP/0RFH mirrors, and a border surface only acts where the two
+  // volumes actually touch. Rounding the offset to float left 0.33 nm of air between them, so
+  // the mirrors never applied and the light left through the side.
+  auto seat = [](Float_t half, Double_t strip) { return double(half) + strip; };
+  double xinv = -seat(ptop[0], prfv[0]);
   topref->AddNode(rfv, 1, new TGeoTranslation(xinv, 0, 0));
-  xinv = ptop[0] + prfv[0];
+  xinv = seat(ptop[0], prfv[0]);
   topref->AddNode(rfv, 2, new TGeoTranslation(xinv, 0, 0));
-  float yinv = -ptop[1] - prfh[1];
+  double yinv = -seat(ptop[1], prfh[1]);
   topref->AddNode(rfh, 1, new TGeoTranslation(0, yinv, 0));
-  yinv = ptop[1] + prfh[1];
+  yinv = seat(ptop[1], prfh[1]);
   topref->AddNode(rfh, 2, new TGeoTranslation(0, yinv, 0));
 
+  // The wrapped radiator, the MCP top glass, the photocathode and the MCP are stacked along z
+  // with no gap between them. Each layer's position is built here from the back face of the one
+  // before it, using the same double addition the box shape uses for its own half-length, so
+  // adjacent faces land on the same double. Summing the float thicknesses in a different order
+  // for each layer, as this code did, left the faces up to 0.24 nm apart.
+  const double zRadiatorCentre = -mInStart[2] + double(ptopref[2]);
+  const double zRadiatorBack = zRadiatorCentre + double(ptopref[2]);
+  const double zTopGlassCentre = zRadiatorBack + double(pmcptopglass[2]);
+  const double zTopGlassBack = zTopGlassCentre + double(pmcptopglass[2]);
+  const double zCathodeCentre = zTopGlassBack + double(preg[2]);
+  const double zCathodeBack = zCathodeCentre + double(preg[2]);
+
   // container for radiator, cathode
   for (Int_t ix = 0; ix < 2; ix++) {
     float xin = -mInStart[0] + 0.3 + (ix + 0.5) * 2 * ptopref[0];
     for (Int_t iy = 0; iy < 2; iy++) {
       float yin = -mInStart[1] + 0.3 + (iy + 0.5) * 2 * ptopref[1];
       ntops++;
-      z = -mInStart[2] + ptopref[2];
-      ins->AddNode(topref, ntops, new TGeoTranslation(xin, yin, z));
-      LOG(debug) << " n " << ntops << " x " << xin << " y " << yin << " z radiator " << z;
-      z += ptopref[2] + 2. * pmcptopglass[2] + preg[2];
-      ins->AddNode(cat, ntops, new TGeoTranslation(xin, yin, z));
-      LOG(debug) << " n " << ntops << " x " << xin << " y " << yin << " z cathod " << z;
+      ins->AddNode(topref, ntops, new TGeoTranslation(xin, yin, zRadiatorCentre));
+      LOG(debug) << " n " << ntops << " x " << xin << " y " << yin << " z radiator " << zRadiatorCentre;
+      ins->AddNode(cat, ntops, new TGeoTranslation(xin, yin, zCathodeCentre));
+      LOG(debug) << " n " << ntops << " x " << xin << " y " << yin << " z cathod " << zCathodeCentre;
     }
   }
   // MCP
   TVirtualMC::GetMC()->Gsvolu("0MTO", "BOX", getMediumID(kOpGlass), pmcptopglass, 3); // Op  Glass
   TGeoVolume* mcptop = gGeoManager->GetVolume("0MTO");
-  z = -mInStart[2] + 2 * ptopref[2] + pmcptopglass[2];
-  ins->AddNode(mcptop, 1, new TGeoTranslation(0, 0, z));
+  ins->AddNode(mcptop, 1, new TGeoTranslation(0, 0, zTopGlassCentre));
 
   TVirtualMC::GetMC()->Gsvolu("0MCP", "BOX", getMediumID(kAir), pmcp, 3); // glass
   TGeoVolume* mcp = gGeoManager->GetVolume("0MCP");
-  z = -mInStart[2] + 2 * ptopref[2] + 2 * pmcptopglass[2] + 2 * preg[2] + pmcp[2];
-  ins->AddNode(mcp, 1, new TGeoTranslation(0, 0, z));
+  ins->AddNode(mcp, 1, new TGeoTranslation(0, 0, zCathodeBack + double(pmcp[2])));
 
   TVirtualMC::GetMC()->Gsvolu("0MSI", "BOX", getMediumID(kMCPwalls), pmcpside, 3); // glass
   TGeoVolume* mcpside = gGeoManager->GetVolume("0MSI");