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Bill,
Unfortunately, I think you have this one wrong. The crystal is a solid
state diode that rectifies the radio-frequency a.c. voltage on the antenna.
(Most kits sold today actually use a diode.) Like all solid-state diodes it
requires a certain forward voltage before it conducts.
Without the LC
circuit, the voltage at the crystal never gets high enough for it to
conduct, so you don't hear anything (the response of the headphones is so
slow that you hear only the modulated envelope of the RF signal when the
radio is working).
What the LC circuit actually does is present to the antenna a very high
impedance at the frequency of interest, this causes the RF voltage to be
high enough to drive the crystal.