Lumbar Disc Herniation: This is the most likely diagnosis given the mechanism of injury (car accident) and the presentation of lower back pain radiating down to one leg. The force of the accident could have caused a disc herniation, leading to nerve root compression and the resulting pain.

Lumbar Strain: The sudden impact of a car accident can cause muscle strain in the lower back, leading to pain that may radiate down the leg due to referred pain patterns.
Lumbar Facet Joint Injury: The facet joints in the lumbar spine can be injured during a car accident, causing pain and stiffness in the lower back that may radiate into the leg.
Sacroiliac Joint Dysfunction: The force of the accident can cause inflammation or injury to the sacroiliac joint, leading to lower back pain that may radiate down into the leg.

Cauda Equina Syndrome: Although less common, this is a medical emergency that requires immediate attention. It involves compression of the cauda equina (nerve roots in the lumbar spine), which can result from a severe disc herniation or other injuries. Symptoms include severe low back pain, bilateral leg pain, numbness, and potentially bladder and bowel dysfunction.
Spinal Fracture: A fracture in the lumbar spine could occur from the trauma of a car accident, leading to instability and potentially severe neurological deficits if not promptly addressed.
Epidural Hematoma: Bleeding into the epidural space surrounding the spinal cord can compress the spinal cord or nerve roots, leading to severe back pain, leg pain, and potentially paralysis if not quickly diagnosed and treated.

Spinal Infection (e.g., Discitis or Osteomyelitis): Although rare, a spinal infection could be a cause of lower back pain, especially if the patient has a compromised immune system or if the infection was introduced during the accident.
Tumor: A pre-existing tumor in the spine could be exacerbated by the trauma of a car accident, leading to new or worsening back and leg pain.
Arterial Injury (e.g., Aortic Dissection): In rare cases, the trauma from a car accident could lead to an arterial injury, such as an aortic dissection, which presents with severe back pain and potentially leg pain due to compromised blood flow.